Question

A spatially uniform magnetic field of $0.080$ $T$ is directed into the plane of the page and perpendicular to it, as shown in the accompanying figure. A wire loop in the plane of the page has constant area $0.010$ m${}^2$. The magnitude of the magnetic field decreases at a constant rate of $3.0\times {10}^{-4}$ T/s. The magnitude and direction of the induced emf is:

• A. $3.0\times {10}^{-6}$ V clockwise
• B. $3.0\times {10}^{-6}$ V anticlockwise
• C. $2.4\times {10}^{-5}$ V anticlockwise
• D. $8.0\times {10}^{-4}$ V clockwise

Answer 1

The correct option is A $3.0\times {10}^{-6}$ V clockwise

$\frac{dB}{dt}=-3\times {10}^{-4}T/s$

$e=-\frac{d\varphi }{dt}$

$e=-A\frac{d\varphi }{do}$

$=-0.010\times (-3\times {10}^{-4})$

$=3\times {10}^{-6}V$

As flux is decreasing in-ward the plane,
$\therefore$ Direction of induced emf will be clockwise