A circular coil of area 0.1 `m^(2)` having 200 turns is placed in a magnetic field of 40 T. The plane of the coil makes `30^(@)` with the field. If the field is removed for 0.1 s then the induced emf in the coil is

Options

A. 4000 V
B. `4000 sqrt(3)V`
C. 2000 V
D. `2000sqrt(3)V`

Answer

B

Explanation

Given, area of circular coil, `A=0.1 m^(2)`
number of turns in the coil, `N=200` turns
and magnetic field, B = 40 T
The angle between plane of the coil and magnetic field, `theta=30^(@)`
`therefore` Flux associated with plane coil in uniform magnetic field is given as,
`therefore " "phi_(1)=NBScostheta " "(because theta=30^(@))`
`" "S=` Area of surface
`" "phi_(1)=200 times 40 times 0.1 times cos30^(@)`
`theta=` angle between the direction of magnetic field and normal to the surface.
`" "=200 times 40 times 0.1 times sqrt(3)/2`
`" "phi_(1)=400sqrt(3)`
When, field removed for 0.1 sec then the flux,
`" "phi_(2)=0`
Net flux, `dphi=phi_(1)-phi_(2)=400sqrt(3)` and dt = 0.1 sec
Now, induced emf in the coil when field is removed for 0.1 sec is
`therefore " "E=(dphi)/(dt)=(400sqrt(3))/0.1`
or `" "E=4000sqrt(3)V`