We can divide the integral on the left-hand side of Ampres law (1) into four integrals, each for one side of the rectangle. We found that the magnetic field. The magnetic field inside the solenoid tends to be uniform which means that field lines due to all the loops are in the same direction which makes the field uniform at all the points inside the solenoid and uniformity increases, even more, when the windings are more tightly bound and also if the number of turns is increased. Because of its shape, the field inside a solenoid can be very uniform, and also very strong. Hence, the given option does not coincide with the correct concept. A solenoid is a tightly wound helical coil of wire whose diameter is small compared to its length. Is it appropriate to ignore emails from a student asking obvious questions. . Thanks! For the first part, since the solenoid is long we can approximate the magnetic field inside to be uniform and is given by $B_z = _0NI$, so we can say that the magnetic field at the center is also $_0NI$. Can several CRTs be wired in parallel to one oscilloscope circuit? Consider any location inside the solenoid, as long as L is much larger than D for the solenoid C Consider only locations along the axis of the solenoid View Available Hint(s) a only b only O conly a and b a and c bandc Weve got your back. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. 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The magnetic field inside a long straight solenoid-carrying current is generally the same at all points inside a magnetic field. Choose the incorrect statements from the following regarding magnetic lines of field. The magnitude of the magnetic field inside the solenoid with n turns per unit length and carrying current I is given by, B = o In so long as the length of the solenoid is much larger than its diameter. The field outside the coils is nearly zero. Solenoid is a current carrying coil. B = oIN / L Where, B is the magnetic fiels of the solenoid I is the current flowing through a solenoid o is vaccum permeability and its value is 1.2610 -7 Tm/A A solenoid has no diameter, and the field inside is constant regardless of where it is located, i.e., where it is positioned. The magnetic field in a solenoid is maximum when the length of the solenoid is greater than the radius of its loops. The answer to this question may be useful: @tmwilson26 Can you expound on the explanation that the user higgsss gave? A cross section of a long solenoid that carries current I is shown. The length of the solenoid is much longer than its diameter, thus we can neglect the imperfections of the field at the ends of the winding. A solenoid is characterized by the number of turns N of the conductor and length of the solenoid l. The density of turns per unit length n is then: We can estimate the arrangement of the magnetic field of the solenoid from the magnetic field of individual loops of the conductor. Ans(9)If you see the diagram as i show . An approximate value. Click hereto get an answer to your question A solenoid that is 95cm long has a radius of 2cm and a winding of 1200 turns; it carries a current of 3.60 A. A solenoid is a long thin loop of wire that is mostly wrapped around a metallic core. Additional information: Solenoid is a coil of wire which is in cylindrical form. We determine its orientation by using the right-hand rule. You join them end to end, such that their magnetic moments are in same direction. A solenoid (/ s o l n d /) is a type of electromagnet formed by a helical coil of wire whose length is substantially greater than its diameter, which generates a controlled magnetic field.The coil can produce a uniform magnetic field in a volume of space when an electric current is passed through it. Shouldnt the magnetic field of a solenoid be affected by length? Consider the solenoid carrying a current 'I' due to which the magnetic field is produced within the solenoid. Counterexamples to differentiation under integral sign, revisited. number of turns N, length, and magnetic field. Magnetic field at the center and ends of a long solenoid [closed], physics.stackexchange.com/questions/95725/, Help us identify new roles for community members. . transcribed image text: magnetic field inside a very long solenoid express your answer in terms of bin , l, and other quantities given in the introduction learning goal: to apply ampere's law to find the magnetic field inside an infinite solenoid b- d: bl submit my answers give up in this problem we will apply ampere's la, written f bg) -d to 1 There are no infinite solenoids. We can thus use the solenoid to create a homogeneous magnetic field, similarly as we use two parallel capacitor plates to create a homogeneous electric field. The best answers are voted up and rise to the top, Not the answer you're looking for? Part A: What is the electric field strength inside the solenoid at a point on the axis? It's a coil whose length is substantially greater than its diameter. A solenoid is a combination of closely wound loops of wire in the form of helix, and each loop of wire has its own magnetic field (magnetic moment or magnetic dipole moment). Why do quantum objects slow down when volume increases? A coil of many circular turns of insulated copper wire wrapped closely in a cylinder's shape is generally known as a solenoid. 1) magnetic field at the center of a long solenoid is given by setting $\theta_1=0$ & $\theta_2=\pi$ $$B=\frac{\mu_0 NI}{2}(\cos 0-\cos\pi)=\color{blue}{\mu_0 NI}$$, 2) magnetic field at the end of a long solenoid is given by setting $\theta_1=\pi/2$ & $\theta_2=\pi$ $$B=\frac{\mu_0 NI}{2}(\cos \pi/2-\cos\pi)=\color{blue}{\frac{\mu_0 NI}{2}}$$. A solenoid is generally easy to wind, and near its center, its magnetic field is quite uniform and directly proportional to the current in the wire. A current of 6.00 A exists in a straight conductor located along the central axis of the solenoid. Is it number of turns or number of turns per unit length? o = Permeability of free space. Find the expression of the force on the electron. (a) At what radial distance from the axis will the direction of the resulting magnetic field be at 45.0 to the axial direction? The line integral of magnetic field vector B along path pqrs is (b) In a toroid, magnetic lines do not exist outside the body./Toroid is closed whereas solenoid is open on both sides./Magnetic field is uniform inside a toroid whereas for a solenoid, it is different at the two ends and cenre The formula to calculate the magnetic field inside a siolenoid is along the lines. Hence, the given concept is an incorrect one. Question 1. Part B: What is the electric field strength inside the solenoid at a point 1.50 cm from the axis? A long solenoid with 10.0 turns/cm and a radius of 7.00 cm carries a current of 20.0 mA. Science Physics An electron is situated at distance d from the axis of a long solenoid. On the other hand, the field lines inside the solenoid are mostly confined to the solenoid's tube and cannot spread our, so the magnetic field inside the solenoid is much . The way he did it, he found the field for a single loop at a distance $z$ from the center of the loop on axis. Complete step by step solution: Inside the solenoid the magnetic field lines are parallel to each other forming a uniform field strength which indicates that the magnetic field is the same at all points inside the solenoid. One end of the solenoid basically acts as a magnetic north pole whereas the other acts as a magnetic south pole. One can make a very long solenoid where the magnetic flux trough the solenoid returns trough a very large volume, which makes the external field small. Amepres law is used to calculate the magnitude of the magnetic \(\vec{B}\)-field in some symmetrical cases, similarly as the Gauss law is used to calculate the magnitude of electric \(\vec{E}\)-field in symmetrical cases in electrostatics. A solenoid is a long conductor that is densely wound to form a cylindrical helix. The magnetic field inside a long straight solenoid-carrying currentis zero.decreases as we move towards its end.increases as we move towards its end.is the same at all points.Answeris the same at all points.Explanation -Inside a solenoid, Field lines are parallel straight linesIt means that magnetic Solenoid Magnetic Field A solenoid is a conductor that is wound into a coil of many turns like a helix. Suppose you have two identical long solenoids, each of them having magnetic field $B$ at the ends. The fields of individual conductor loops sum up to the total field of the solenoid. the solenoid is zero. Advanced Physics. Rather it is said to remain the same at all points inside a magnetic field. The magnetic field is constant throughout a solenoid's entire body, which is infinitely long. The magnetic field lines inside a solenoid are in the form of parallel straight lines. The magnetic field is calculated at any point in space by summing up the magnetic fields generated by each turn of a wire. Homework help starts here! We assess the magnitude of the magnetic B-filed by using Ampres law: We use a rectangle denoted ABCD as the Ampres curve, with two sides of length h parallel to the axis of the solenoid. Outside the solenoid, the magnetic field is far weaker. How can you know the sky Rose saw when the Titanic sunk? since you are concerned about a long solenoid, this problem has a very simple solution. When would I give a checkpoint to my D&D party that they can return to if they die? Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. Although we derived the formula of the magnitude of the magnetic B-field. So that the field at both ends are NI/2. Using the formula for the magnetic field inside an infinite solenoid and Faraday's law, we calculate the induced emf. The magnetic fields of a solenoid are determined by the density of coils, the number of turns, and the current flowing through it. [/B] Reply Answers and Replies Dec 11, 2014 #2 A cross section of a long solenoid that carries current. PSE Advent Calendar 2022 (Day 11): The other side of Christmas. I'm not sure if my argument is correct but based on my understanding, from the uniformity of the $B$-field inside, it should be the same everywhere inside. Magnetic Field inside a Solenoid Collection of Solved Problems Thermodynamics Optics Magnetic Field inside a Solenoid Task number: 1785 Derive the formula for the amplitude of the magnetic B -field of a solenoid that has n turns per 1 m of its length and is carrying a current I. The contributions from opposite sides of each individual turn of the conductor outside of the solenoid act against each other and the field is much less intensive than inside the solenoid. Details of the calculation: B = (4*10 -7 N/A 2 )*30 A/ (2*0.01 m) = 1.2*10 -5 /*0.02 = N/ (As) = 5*10 -4 T. For comparison, near Knoxville, TN, the strength of the Earth magnetic field is ~ 53 microT = 5.3*10 -5 T. d. The magnitude of B is proportional to the number of turns of wire per unit length. Advanced Physics questions and answers. MP9-2: Force on Moving Charges in a Magnetic Field; MP9-2: Ampre's Law Explained; MP9-2: Magnetic field from current segments (spoiler) MP9-2: Electromagnetic velocity filter (spoiler) MP9-1: Magnetic field at the center of a wire loop. We have derived that the magnitude of the magnetic field inside the solenoid with a given density of turns does not depend on the diameter of the solenoir and is the same everywhere in the cross-section of the solenoid. The magnetic field inside a long straight solenoid-carrying current is generally the same at all points inside a magnetic field. Definition 2 A. A 10 turn coil is wrapped tightly around the circumference of the solenoid . Magnetic Field Produced by a Current-Carrying Solenoid A solenoid is a long coil of wire (with many turns or loops, as opposed to a flat loop). Because there are straight lines leading from the center to the poles of a solenoid, the magnetic field inside is uniform. How do I put three reasons together in a sentence? The term solenoid was coined in 1823 by Andr-Marie Ampre. Figure 12.7. Therefore, the value of magnetic field inside the solenoid is and outside . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Determine the magnetic field produced by the solenoid of length 80 cm under the number of turns of the coil is 360 and the current passing through is 15 A. for an infinitely long ideal solenoid, it is valid also for a real solenoid of finite length as long as we are interested in the field sufficiently far from its ends. Physical Principles We learned that the magnitude field inside a solenoid is uniform, and its strength B can be calculated as "B = 0nI" where I is the current flowing through the solenoid's wire, n is turns density, which equals the number of turns (wire loops) across L of the solenoid, 0 is the magnetic permeability of space (1.26 10-6 T . Also, why magnetic field inside a solenoid is uniform? Magnetic Field Question 3 Detailed Solution Concept : Magnetic Field Inside a toroid is given as : B = oni where, n = N 2 R w hich is the turn density. Yes, those are the correct relationships. Magnetic Effects of Electric Current Class 10 MCQs Questions with Answers. The magnetic field generated in the centre, or core, of a current carrying solenoid is essentially uniform, and is directed along the axis of the solenoid. The mathematical formulation of Ampres law is: where I denotes the total electric current passing through Ampres curve l. We can assess the distribution of the magnetic field of the solenoid from the magnetic field of individual turns of the conductor. Thus, at the junction the magnetic field adds up to $B+B=2B$. The magnetic field inside a long straight solenoid-carrying current (a) is zero (b) decreases as we move towards its end (c) increases as we move towards its end (d) is the same at all points, The magnetic field lines inside a long, current carrying solenoid are nearly. An approximate value for the magnitude e. What is the magnitude of the magnetic field inside a 0.5 m long solenoid having 163 loops with a current of 11.9 kAWhat is the magnitude of the induced current in a loop of wire having resistance 63.2 Ohms if the change in flux is 21.8 W in 7.9 ms? The magnetic B-field inside a solenoid with n turns per unit length carrying a current I is: Choose required ranks and required tasks. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. i = Current flowing through the wire. But is my answer for the first part correct? The field lines inside the solenoid are known to be parallel and straight. R = Radius of the circular loop. The magnetic field lines inside the toroid are concentric circles. Magnetic fields are produced by electric currents; a simple segment of current-carrying wire will generate around it a circular magnetic field in accordance with the right hand rule. Derive the formula for the amplitude of the magnetic B-field of a solenoid that has n turns per 1m of its length and is carrying a current I. Because they can transform electric current into mechanical motion, solenoids are frequently employed in switches. Then we solve for the electric field. Calculate the magnitude of the magnetic field inside the solenoid. Is it possible to hide or delete the new Toolbar in 13.1? Magnetic field = permeability x turn density x current. Magnetic field of a solenoid at the poles? (a) from the diagram we can say that when we curl our fingers along current th. If we have a long solenoid of length L, current I, and total number of turns N, what is the magnetic field inside the . If the current in the solenoid is I = amperes. How to get the magnetic field strength in space near a solenoid, Magnetic field very far from long solenoid, Magnetic field around solenoid and toroid. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. More loops will bring about a stronger magnetic field. Hint Solenoid Hint Magnetic field of a solenoid If you are doing the long solenoid approximation, you can take the limit of $L\rightarrow \infty$. N is the number of turns per unit length. Solenoids are commonly used in experimental research requiring magnetic fields. A solenoid can be used as an electromagnet when the ends are connected to a battery. What is the effect of introducing an iron core in a long solenoid on magnetic field? Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. Inside the coil the field is very uniform, and the field from a solenoid is essentially identical to the field from a bar magnet. Also, find the magnetic field at the ends of the solenoid. Homework Equations U= (1/2)LI^2 => U = (1/2) (B^2) (area*length)/ (u) The Attempt at a Solution We can check our result against something else we know: The circulation of the vector potential around the solenoid should be equal to the flux of B inside the coil (Eq. The magnetic field in the solenoid is the product of the current flowing through the solenoid and the number of turns of the wire per unit length of the solenoid. A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. For a long, thin solenoid, the magnetic field lines outside the solenoid spread out in all 3 dimensions, so the magnetic field outside the solenoid's wall is fairly weak. The magnetic field within a solenoid depends upon the current and density of turns. Try BYJUS free classes today! 1 shows a solenoid consisting of N turns of wire tightly wound over a length L. Solution: Given: Number of turns N = 360 Current I = 15 A Permeability o = 1.26 106 T/m Length L = 0.8 m The magnetic field in a solenoid formula is given by, B = oIN / L d. The magnitude of \( \mathbf{B} \) is proportional to the number of turns of wire per unit length. Energy Stored in Magnetic Field of Solenoid x^2 Apr 16, 2009 Apr 16, 2009 #1 x^2 21 1 Homework Statement The magnetic field inside an air-filled solenoid 39.9cm long and 2.00cm in diameter is 0.800T. @HarishChandraRajpoot Can you please include or add a source for the derivation of that general formula please ? So, we can say that the magnetic field inside a long ideal solenoid depends on three main factors. For the second part I don't have any idea on how to start. N = Number of Turns. A long solenoid has current $I$ flowing through it, also denote $N$ as the turns per unit length. So by this way we can determine the magnetic field inside a solenoid, like mentioned before, it either can be due the absence of current and the long solenoid. It produce a uniform magnetic field in a volume of space when an electric current is passed through it. B = I/2r ( Magnetic field at the centre of a current carrying coil) The Attempt at a Solution B = I/2r Let the number of turns per unit length of the solenoid be 'n' and its length be 'a' So, B = naI/2r Which is definitely not equal to nI (Calculated using Ampere's Circuital Law) What's wrong? He then integrated the field of many loops at different positions. The magnetic field of a solenoid is given by the formula: B = oIN/L Find the magnetic field at the center of the solenoid (on the axis). A cross section of a long solenoid that carries current \( I \) is shown. The field at the center of a LONG solenoid is the same field everywhere inside, which is NI? Find the magnetic field at the center of the solenoid (on the axis). The magnitude of the magnetic field field a radial distance r away from a long, straight wire is B = 0 I/ (2r). Experts are tested by Chegg as specialists in their subject area. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Calculate the magnitude of the axial magnetic field inside the solenoid. We want our questions to be useful to the broader community, and to future users. It has been found that if a soft iron rod called core is placed inside a solenoid, then the strength of the . Thus, the magnetic field at the center of a long solenoid is two times the magnetic field at the ends . But this junction is nothing but the mid point of another long sloenoid, with same value of N. Thus we get $NI=2B$, or $B=NI/2 $! Click to see full answer . Can anyone kindly tell me if this is correct? Books that explain fundamental chess concepts. The field just outside the coils is nearly zero. What is the relationship of the field at the ends to the center? For a solenoid of length L = m with N = turns, the turn density is n=N/L = turns/m. Magnetic Field Inside Solenoid Example 11,190 views Dec 13, 2013 59 Dislike Share Save Andrey K 669K subscribers Donate here: http://www.aklectures.com/donate.php Website video link:. We asses the magnetic field inside the toroid using the formula for the magnetic field in a solenoid because a toroid is in fact a solenoid whose ends are bent together to form a hollow ring. Magnetic Field of a Solenoid You can create a stronger, more concentrated magnetic field by taking wire and forming it into a coil called a solenoid. Field Inside the solenoid: Consider a closed path pqrs. 14.11 ). Therefore, the answer is Option A . $$B=\frac{\mu_0 NI}{2}(\cos\theta_1-\cos\theta_2)$$ Take its axis to be the $z$-axis, by symmetry the only component of the magnetic field inside is $B_z$. rev2022.12.11.43106. (please provide your answer to . And as we know that current creates magnetic field around it, the solenoid also creates magnetic field. Solenoids can convert electric current to mechanical action, and so are very commonly used as switches. Give the BNAT exam to get a 100% scholarship for BYJUS courses. The core of a solenoid produces a magnetic field when an electric current passes through it. 2003-2022 Chegg Inc. All rights reserved. If an electron was to move with a speed of 104 m/s along the axis of this current carrying solenoid, what would be the force experienced by this electron? In the limit the ratio between internal and external field volume goes to infinity, but that's a mathematical trick that has no physical equivalent. Magnetic Field of a Solenoid Solenoids have many practical implications and they are mainly used to create magnetic fields or as electromagnets. We determinde the field inside the solenoid using Ampres law (see the Hint). (a) the direction of magnetic field at a point is taken to be the direction in which the north pole of a magnetic compass needle points. The magnetic field inside the long straight solenoid can be shown as: The magnetic field inside a long straight solenoid-carrying current is not considered as zero, rather it is generally known to be the same at all points inside a magnetic field. CGAC2022 Day 10: Help Santa sort presents! Calculation: Given: For Toroid 1 N1 = 200 turns R1 = 40cm = 4010-2 m Notice, the magnetic field at some internal point on the axis of a solenoid is given by general expression This equation is used to obtain the magnitude of the magnetic field inside a long solenoid. A long solenoid of cross-sectional area \(5.0 \, cm^2\) is wound with 25 turns . Magnetic field inside a cylindrical solenoid A solenoid is comprised of multiple current loop wrapped in the form of a cylindrical tube. Solenoid Magnetic Field Calculation. b. If the magnetic field inside the solenoid is 0.3 T, then megnetic force on the wire isa)0.14 Nb)0.24 Nc)0.34 Nd)0.44 NCorrect answer is option 'B'. The number of turns N refers to the number of loops the solenoid has. Also, find the magnetic field at the ends of the solenoid. A solenoid has a cross sectional area of 6.010 4m 2, consists of 400 turns per meter , and caries current of 0.40 A. See our meta site for more guidance on how to edit your question to make it better. 5.42 appropriate to surface currents) to find the field inside and outside an infinitely long solenoid of radiusR, with n turns per unit length, carrying a steady current I. . Approximately how much energy is stored in this field? Solution Show Answer Significance Why does the USA not have a constitutional court? So the field at both ends of the solenoid is half of the field at the center? Magnetic field in a long solenoid is homogeneous and its strength doesn't depend on the distance from the axis or on the cross-sectional area of the solenoid. No worries! In the United States, must state courts follow rulings by federal courts of appeals? Active formula: click on the quantity you wish to calculate. It is pointed in a curled-straight, right-hand direction along the axis. Analysis. The winding is adequately tight so that each turn is well approximated as a circular wire loop lying in a plane perpendicular to the solenoid's axis. He started at $z=0$ and ended at $z=L$ for his integrals. X X X -d. x X X X X B 130 y X. If you wish to filter only according to some rankings or tags, leave the other groups empty. A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. @tmwilson26 Thank you for the clarification! Here you can find the meaning of An 8 cm long wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. More loops will bring about a stronger magnetic field. Science. where, $\theta_1$ & $\theta_2$ are the angles between axis & the lines joining the extreme-points of both the ends of solenoid to the concerned point. The magnetic field is uniform for long solenoids only. For the first part, since the solenoid is long we can approximate the magnetic field inside to be uniform and is given by B z = 0 N I, so we can say that the magnetic field at the center is also 0 N I. B is directed to the left. Since we have cylindrical symmetry, the electric field integral reduces to the electric field times the circumference of the integration path. It carries a current of 5 A. All of the following statements about the magnetic field B inside the solenoid are correct EXCEPT: a. Any suggestions and insights? Why do we use perturbative series if they don't converge? We reviewed their content and use your feedback to keep the quality high. The end of the coil are connected to a 1.5 resistor. In the case of a sufficiently long and densely wound coil (which is the informal definition of the solenoid), the magnetic field of all turns of the conductor sum so that there is a homogeneous total magnetic field inside the solenoid. A solenoid refers to a coil of wire which is insulated, and wound on an object which is in the shape of a rod made of iron or solid steel. Is there a higher analog of "category with all same side inverses is a groupoid"? We consider the field outside the solenoid to be approximately zero and the field inside the solenoid to be approximately homogeneous (as derived in the previous section in more detail). The number of turns N refers to the number of loops the solenoid has. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time 0.050 s. Outside of the centre, the magnetic field lines are farther apart and the fields are weaker. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. When a current passes through it, it creates a nearly uniform magnetic field inside. The vector of the magnetic B-field inside the solenoid directs along the axis of the solenoid. The first integral on the right-hand side of equation (2) is: The second and the fourth integrals are equal to zero because the vector of the magnetic \(\vec{B}\)-field is either perpendicular to path section \(\mathrm{d}\vec{l}\) and thus the scalar product along the rectangle sides BC and DA is zero: The third integral along the rectangle side CD is almost zero as the magnetic field is negligible outside the solenoid. The formula for the field inside the solenoid is B = 0 I N / L where B is the magnetic field, N is the number of turns in the solenoid, I is the current in the coil, L length of the coil. 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The magnetic field inside a current carrying solenoid is: Medium View solution > The strength of magnetic field inside a long current carrying straight solenoid is: Easy View solution > View more More From Chapter Moving Charges and Magnetism View chapter > Revise with Concepts Magnetic Field Due to Solenoid Example Definitions Formulaes It follows that we can the neglect the outer field in the case of a very long solenoid. The magnetic field inside a long straight solenoid-carrying current neither increases nor decreases as we move toward its end. So the magnetic field outside a very long solenoid is indeed zero, even though the vector potential is not. Transcribed image text: To apply Ampere's law to find the magnetic field inside an infinite solenoidi In this problem we will apply Ampere's law, written integral B vector vector middot dl vector = mu_0 I_encL, to calculate the magnetic field inside a very long solenoid (only a relatively short segment of the solenoid is shown in the pictures). (b) magnetic field lines are closed . b. The Field from a Solenoid. A solenoid is simply a coil of wire with a current going through it. \[\int_l \vec{B}\cdot \,\mathrm{d}\vec{l}=\mu_o I_c,\], \[\int_l \vec{B}\cdot \,\mathrm{d}\vec{l}=\mu_o I_c.\tag{1}\], \[\int_{ABCD} \vec{B}\cdot \,\mathrm{d}\vec{l}=\int_{A}^{B} \vec{B}\cdot \,\mathrm{d}\vec{l}+\int_{B}^{C} \vec{B}\cdot \,\mathrm{d}\vec{l}+\int_{C}^{D} \vec{B}\cdot \,\mathrm{d}\vec{l}+\int_{D}^{A} \vec{B}\cdot \,\mathrm{d}\vec{l}.\tag{2}\], \[\int_{A}^{B} \vec{B}\cdot \,\mathrm{d}\vec{l}=Bh.\], \[\vec{B}\,\cdot\, \mathrm{d}\vec{l}=0.\], \[\int_l \vec{B}\cdot \,\mathrm{d}\vec{l}=Bh.\], Tasks requiring comparison and contradistinction, Tasks requiring categorization and classification, Tasks to identify relationships between facts, Tasks requiring abstraction and generalization, Tasks requiring interpretation,explanation or justification, Tasks aiming at proving, and verification, Tasks requiring evaluation and assessment, Two balls on a thread immersed in benzene, Electric Intensity at a Vertex of a Triangle, A charged droplet between two charged plates, Capaciter partially filled with dielectric, Electrical Pendulum in Charged Spheres Field (Big Deflection), Gravitational and electric force acting on particles, Field of Charged Plane Solved in Many Ways, Electric resistance of a constantan and a copper wire, Electrical Resistances of Conductors of Different Lengths, Electrical Resistance of Wires of Different Cross Sections, Measuring of the electrical conductivity of sea water, Two-wire Cable between Electrical Wiring and Appliance, Using Kirchhoffs laws to solve circiut with two power supplies, Change of the current through potentiometer, Application of Kirchhoffs laws for calculation of total resistance in a circuit, Current-carrying wire in a magnetic field, Magnetic Force between Two Wires Carrying Current, Magnetic Field of a Straight Conductor Carrying a Current, Magnetic Field of a Straight Conductor inside a Solenoid, The motion of a charged particle in homogeneous perpendicular electric and magnetic fields, Voltage Induced in a Rotating Circular Loop, Inductance of a Coil Rotating in a Magnetic Field, The Length of the Discharge of the Neon Lamp, Instantaneous Voltage and Current Values in a Series RLC Circuit, RLC Circuit with Adjustable Capacitance of Capacitor, Heating Power of Alternating Current in Resistor, Resonance Frequency of Combined Series-Parallel Circuit. 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