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.

The current in the loop is  

Explanation:

From the question we are told that

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

         The radius is given as R

           Let denote the constant unknown current as  

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

And its direction is the positive z-direction  So

The  potential energy is mathematically represented as

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

     For the loop the initial potential energy is

     The final potential energy is

                  the 180° showing the loop is flipped over  

 The change in the Potential energy give the workdone

Let denote this workdone with W So,

Making the current subject of the formula we have

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