Answer correctly and completely if you want a good review 1. What is the magneti
ID: 1471840 • Letter: A
Question
Answer correctly and completely if you want a good review
1. What is the magnetic field at the center of the small loop due to the current in the large loop at t = 0? Take B as positive if out of the paper.
2.)What is the magnetic field at the center of the small loop due to the current in the large loop at t = 0.50 s? Take B as positive if out of the paper.
3.)What is the magnetic field at the center of the small loop due to the current in the large loop at t = 1.00 s? Take B as positive if out of the paper.
4.)What emf is induced in the small loop at t = 0.50 s? Take emf as positive if counterclockwise. Note that since the inner loop is small, you can assume that the B field due to the outer loop is uniform over the area of the smaller loop.
Explanation / Answer
The equation for the current as a function of time is given by
I = Io (1 - 2t)
The magnetic field at the center of a current loop is given by
B = (uo * I)/2*R
At t = 0, the current is 200 A, so the magnetic field is given by
B = (uo * I)/2*R
B = (4*PI*10^-7 * 200) / (2 * 1)
B = 1.26 * 10^-4 T
2.)
At t = 0.5 s, the current is 0 A, so the magnetic field is zero.
B = 0
3.)
At t = 1, the current is -200 A, so the magnetic field is given by
B = - 1.26 * 10^-4 T
4.)
The magnetic flux through the loop is given by , = B.A
Change in magnetic flux over time is known as the EMF. Therefore we can write
emf e = d/dt ()
e = d/dt * (B.A)
e = d/dt * (uo*I*A/ 2R)
e = (uo*A/2*R) * dI/dt
di/dt = -200 - 200 = - 400A
Substituing Values,
e = (4*pi*10^-7 * 7 * 10^-4)/(2*1.0) * (-400)
e = - 1.759 * 10^-7 V
Emf induced in the small loop, e = - 1.759 * 10^-7 V