Question

A square loop of side $10\, cm$ and resistance $5 \,Ohm$ 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. $1 \,mV$
• B. $10 \,mV$
• C. $100 \,mV$
• D. $1 \,V$

Answer 1

Answer: (B)

$10 \,mV$

Answer 2

Side of square loop $=10\,cm=0.1\,m$
Area of square loop, $A=0.01\,m^{2}$
Magnetic field of loop $=1\,T$
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, $\phi=AB\,cos\,\theta$
$=(0.01) (1) \, cos\,45^{\circ}$
$=0.007 =7 \times 10^{-3}\,Wb$
The magnetic field is reduced to zero in time $0.7\,sec$
So,induced emf is, $e=\frac{d\phi}{dt}$
$=\frac{7\times10^{-3}}{0.7}$
$\frac{1}{100}V$
$=10\,mV$