A circular loop of wire with radius R is in a uniform magnetic field with magnitude B that points in the positive z-direction. The loop is i

Question

A circular loop of wire with radius R is in a uniform magnetic field with magnitude B that points in the positive z-direction. The loop is initially in the xy-plane and carries a constant, unknown current. Flipping the loop over requires you to do positive work (W). Determine the current in the loop.

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Latifah 3 years 2021-08-13T14:16:14+00:00 1 Answers 1 views 0

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  1. King
    0
    2021-08-13T14:17:45+00:00
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    Answer:

    The current in the loop is  I = \frac{W}{2 \pi R^2 B}

    Explanation:

    From the question we are told that

              The magnetic field(B) points in a positive z direction so mathematically

                      B = 0\r i + 0\r j + B\r k

                         = B\r k

             The radius is given as R

               Let denote the constant unknown current as  I

    Generally the magnetic dipole moment of the field is mathematically represented as

                           \mu = IA

    And its direction is the positive z-direction  So

                       \mu = IA \r k

                        A = \pi R^2

    The  potential energy is mathematically represented as

                   V = - \mu B cos \theta

    The negative sign show that it increases when work is done against the field  

         For the loop the initial potential energy is

                V_i = -\mu B cos (0)

                   =-I \pi R^2 B

         The final potential energy is

                 V_f = -\mu B cos(180)     the 180° showing the loop is flipped over  

                     =I \pi R^2 B

     The change in the Potential energy give the workdone

    Let denote this workdone with W So,

                    W = V_f -V_i

                        = I \pi R^2 B - (-I \pi R^2 B)

                        = 2 \pi I R^2 B

    Making the current subject of the formula we have

                   I = \frac{W}{2 \pi R^2 B}

                 

                     

                                   

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