Question

A flat square loop with a side a = 20 cm is placed in a magnatic field B = $(a+\beta t^2)$ Where $\alpha$ and $\beta$ are constants and the plane of the loop is at right to B. Find the induced emf generated in the loop at time t = 5

• A. 0.4 $\beta$ V
• B. 0.4 V
• C. 0 . 8 V
• D. 0.16 $\beta$ V

Answer 1

The correct option is A 0.4 $\beta$ V

Given,

Magnetic field $B=\alpha +\beta t^2$

Area of square$=a^2$

Time, $t=5\sec$

$emf=\frac{-d\varphi }{dt}=\frac{-AdB}{dt}=\frac{-Ad(\alpha +\beta t^2)}{dt}=-2A\beta t$

$emf=-2\times {0.2}^2\beta \times 5=-0.4\beta V$

Emf generate in square loop is $0.4\beta V$.