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

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