Question

Uniform magnetic filed B = 10 T is acting in a region of length L = 2m as shown. A square loop of side $\frac{L}{2}$ enters in it with constant acceleration $a=1m/s^2$. Resistance per unit length of the square frame is $\frac{1\Omega }{m}$. At, t = 1s

• A. Induced current in the square frame is clockwise
• B. Induced current in the frame is 2.5 A
• C. Magnetic force on the frame is 25 N
• D. Magnetic torque on the frame is zero

Answer 1

Answer: (B), (C), (D)

The correct options are
B

Induced current in the frame is 2.5 A

C

Magnetic force on the frame is 25 N

D

Magnetic torque on the frame is zero

After 1 second distance moved by the wire frame is $A=\frac{1}{2}\times a{t}^2=0.5m$

Speed, v = at = 1 m/s
Total resistance $=4\Omega$
Induced emf $=Bv\left(\frac{L}{2}\right)=10\times 1\times 1=10V\therefore i=\frac{10}{4}$
= 2.5 A
$F_m=iB\frac{L}{2}=2.5\times 10\times 1=25N$.

During entering in the magnetic field Ä magnetic flux passing through the frame is increasing. Hence, from Lenz’s law, induced current will produce magnetic field or current will be anticlockwise. Torque will be zero as and are antiparallel.