Question

A square loop of wire, side length 10 cm is placed at angle of ${45}^o$ with a magnetic field that changes uniformly from 0.1 T to zero in 0.7 seconds. The induced current in the loop ( its resistance is $1\Omega$) is

• A. 1.0 mA
• B. 2.5 mA
• C. 3.5 mA
• D. 4.0 mA

Answer 1

The correct option is A 1.0 mA

$L=10cm={10}^{-2}m$ ,$\theta =45$

Initial magnetic field $B_i=0.1T$

Final magnetic field $B_f=0T$

$\Delta t=0.7s$ ,$R=1\Omega$

Now ${\varphi }_B=BA\cos \theta =\frac{{10}^{-3}}{\sqrt{2}}$wB

${\varphi }_{B_f}=0wb$

$\epsilon =\frac{\left|\Delta {\varphi }_B\right|}{\Delta t}=\frac{{10}^{-3}}{\sqrt{2}}\times \frac{1}{0.7}=1mV$

$I=\frac{\epsilon }{R}=\frac{1mV}{1\Omega }=1mA$