Question

A square loop of side 22cm is changed to a circle in time 0.4 sec with its plane normal to a inagnetic field 0.2T. The emf induced is

• A. +6.6mv
• B. -6.6mv
• C. +13.2mv
• D. -13.2mv

Answer 1

Answer: (B)

-6.6mv

Answer 2

Given:
The side length of the square loop, L = 0.22m
Time taken for transformation, $\Delta t = 0.4$s
Magnetic field strength, B = 0.2T
The angle between the magnetic field and normal to the plane, $\theta = 90^\circ$

Area of the square loop, $A_{\mathrm{s}} = L^2 = 0.0484 \mathrm{~m}^2$
Area of the circle, $A_{\mathrm{c}} = \pi \left( \frac{L}{2\pi} \right)^2 = 0.00385 \mathrm{~m}^2$

Change in area, $\Delta A = A_{\mathrm{c}} - A_{\mathrm{s}} = 0.00385 \mathrm{~m}^2 - 0.0484 \mathrm{~m}^2 = -0.04455 \mathrm{~m}^2$

Now, calculate the induced emf:
$\varepsilon = \frac{\Delta \varphi_{\mathrm{B}}}{\Delta t} = \frac{B \Delta A \cos \theta}{\Delta t} = \frac{0.2 \times (-0.04455)}{0.4} = -6.66 \mathrm{~mV}$

So, the correct option is (B): -6.6mV