Question

A square loop of side $12cm$ and resistance $0.60\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of $0.10T$ is set up across the plane in north-east direction. The magnetic field is decreased to zero in $0.6s$ at a steady rate. The magnitude of current during this time interval is

• A. $1.42\times 10^{-3}A$
• B. $2.67\times 10^{-3}A$
• C. $3.41\times 10^{-3}A$
• D. $4.21\times 10^{-3}A$

Answer 1

Answer: (B)

Here, Area $A=l^2=(12cm{)}^2$
$=1.4\times 10^{-2}{m}^2$
$R=0.60\Omega$,
$B_1=0.10T$,
$\theta =45^{\circ }$
$B_2=0$,
$dt=0.6s$
Initial flux, ${\varphi }_1=B_{1}Acos\theta$
$=0.10\times 1.4\times 10^{-2}\times cos45^{\circ }$
$=9.8\times 10^{-4}Wb$
Final flux, ${\varphi }_2=0$
Induced emf, $\epsilon =\frac{|d\varphi |}{dt}=\frac{|{\varphi }_2-{\varphi }_1|}{dt}$
$=\frac{|9.8\times 10^{-4}|}{0.6s}=1.6\times 10^{-3}V$
Current, $I=\frac{\epsilon }{R}=\frac{1.6\times 10^{-3}}{0.6}$
$2.67\times 10^{-3}A$