Uniform magnetic field B =5 T is acting in the region of length L=5 m as shown in Fig. A square loop of side `L//5` enters in it with constant acceleration `a =1 m s^(-2)`. Resistance per unit length of the square frame is `1 (Omega) m^(-1)`. At t = 1 s

Options

A. Induced current in the square frame is anti-clockwise.
B. Induced current in the frame is 1.25 A
C. Magnetic force on the frame is 6.25 N.
D. Magnetic torque on the frame is zero

Answer

A, B, C, D

Explanation

While the frame enters the magnetic field, magnetic flux through the frame is increasing. Hence from Lenz's law, induced current will be anticlockwise.
So, choice (a) is correct.
After 1 sec, distance moved by frame
`S= 1/2 at^(2)`
`S=1/2 xx 1 xx 1^(2)=0.5 m`
and speed `v=at = 1 xx 1 =1 m//s`
Induced emf =`Bv(L)/(5)`
`=5 xx 1 xx 1 =5V`.
Hence indcued current
`i=(epsilon)/(R)=5/4 = 1.25 A`
(resistance of loop=`4 Omega`)
so, choice (b) is correct.
force `F=iB(L)/(5)=1.25 xx 5 xx 1 = 6.25 N`
Since magnetic moment and magnetic field are anti-parallel so torque will be zero. so, choice (d) is correct.
Hence choice (a),(b),(c) and (d) are correct.