A coil of 1200 turns and mean area of 500 cm 2 is held perpendicular to a uniform magnetic field of induction 4 × 10-4 T. The resistance of the coil is 20 Ω. When the coil is rotated through 180° in the magnetic field in 0.1 s the average electric current (in mA ) induced is:

Question

A coil of 1200 turns and mean area of 500 cm 2 is held perpendicular to a uniform magnetic field of induction 4 × 10-4 T. The resistance of the coil is 20 Ω. When the coil is rotated through 180° in the magnetic field in 0.1 s the average electric current (in mA ) induced is: (A) 12 (B) 24 (C) 36 (D) 48

Tardigrade Admin · Accepted Answer

Magnetic flux linked with the each turn of coil

ϕ_{1} = B A

as coil is perpendicular to B)
On rotating coil through

18 0^{\circ}

,
Flux linked

ϕ_{2} = - B A

∴

Change in magnetic flux

Δ ϕ = ϕ_{2} - ϕ_{1} = - 2 B A

So, emf induced in the coil

e = - N \frac{Δ ϕ}{Δ t} = \frac{2 NB A}{Δ t}

where,

N

is the number of turns in the coil.
The current in the coil is given by:

i = \frac{e}{R} = \frac{2 NB A}{R Δ t}

= \frac{2 \times 1200 \times 4 \times 1 0 ^{- 4} \times 500 \times 1 0 ^{- 4}}{20 \times 0.1}

= 24 \times 1 0^{- 3} A = 24 m A

$12$

$24$

$36$

$48$

Q. A coil of 1200 turns and mean area of 500cm2 is held perpendicular to a uniform magnetic field of induction 4×10−4T. The resistance of the coil is 20Ω. When the coil is rotated through 180∘ in the magnetic field in 0.1s the average electric current (in mA ) induced is:

12

24

36

48

$12$

$24$

$36$

$48$