Question

A square loop of side $10cm$ and resistance $5Ohm$ is placed vertically in East-West plane. A uniform magnetic field of $1$ Tesla is set across the plane in North-East direction. The magnetic field becomes Zero in $700$ ms at a steady rate. The magnitude of induced $emf$ during this interval is

• A. $1mV$
• B. $10mV$
• C. $100mV$
• D. $1V$

Answer 1

Answer: (B)

Side of square loop $=10cm=0.1m$
Area of square loop, $A=0.01m^2$
Magnetic field of loop $=1T$
The square loop is placed vertically in the east-west plane and the magnetic field is applied along north-east direction. So angle between area vector and magnetic field is, $\theta =45^{\circ }$.
The flux through the loop, $\varphi =ABcos\theta$
$=(0.01)(1)cos45^{\circ }$
$=0.007=7\times 10^{-3}Wb$
The magnetic field is reduced to zero in time $0.7sec$
So,induced emf is, $e=\frac{d\varphi }{dt}$
$=\frac{7\times 10^{-3}}{0.7}$
$\frac{1}{100}V$
$=10mV$