The magnetic field at the center of a 0.500-cm-diameter loop is 2.00 mT .

Question

What is the current in the loop?

Answer 1

Hi Tyler A.!

The magnetic field of a loop is given by:

B = Nμ_oI/2r

Where:

1. N is the number of loops
2. μ_o is the permeability of free space

In our example above, we can reasonably deduce that there is only one loop. In which case, N = 1 and we need not include it our equation:

B = μ_oI/2r

We already have most of the information required to answer this question. However, we must first convert the diameter into the radius:

d = 2r => r = (1/2)d

<=> (1/2)(0.5cm)

r = 0.25 cm = 2.5x10^-3 m

Now, we simply rearrange our equation and solve for the current:

B = μ_oI/2r => I = B(2r)/μ_o

=> μ_o = 4*pi x 10^-7 T*m*A^-1 = 1.25x10^-6 T*m*A^-1

<=> [(2.00x10^-3 T)(2*2.5x10^-3 m)]/(4*pi x 10^-7 T*m*A^-1)

I = 7.996 A

Hope this helps!

Cheers