Question

A 10-turn square coil 0.50 m on a side lies in the xy-plane. A uniform magnetic field with magnitude 1.0 T in the negative z-direction changes steadily to 3.0 T in the positive z-direction, a process that takes 2.0 s. What is the magnitude of the induced emf in the coil?

Answer 1

Answer:

The magnitude of the induced emf in the coil is 5 volts.

Explanation:

Faraday's law states that an induced emf on a coil is:

$\xi=-N\frac{d\varphi_{B}}{dt}$ (1)

with $\frac{d\varphi_{B}}{dt}$ the change of magnetic flux on time and N the number of turns

Because magnetic field is perpendicular to the coil magnetic flux is $\varphi_{B}=BA$ with B the magnetic field and A the area of the coil, so the change on magnetic flux is $\mid (3.0T)(0.5m)^2-(-1.0T)(0.5m)^2\mid$ over a period of 2.0s is $\frac{\mid (3.0T)(0.5m)^2-(-1.0T)(0.5m)^2\mid}{2s}=\frac{1Tm^2}{2s}$.

Using that value on (1):

$\xi=-(10)\frac{1}{2}$

Because we're interested on the magnitude the minus sign on the equation is not important here, so:

$\mid \xi \mid =(10)\frac{1}{2}=5V$