A coil has 1000 turns and 500 cm 2 as its area. The plane of the coil is placed perpendicular to a uniform magnetic field of 2 × 10-5 T. The coil is rotated through 180° in 0.2 seconds. The average emf induced in the coil, in mV is

Question

A coil has 1000 turns and 500 cm 2 as its area. The plane of the coil is placed perpendicular to a uniform magnetic field of 2 × 10-5 T. The coil is rotated through 180° in 0.2 seconds. The average emf induced in the coil, in mV is (A) 5 (B) 10 (C) 15 (D) 20

Tardigrade Admin · Accepted Answer

When the plane of a coil is perpendicular to the field, the flux linked with the coil is

ϕ_{1} = NB A cos 0^{\circ} = NB A

When the coil is turned through

18 0^{\circ}

, the flux linked with the coil is

ϕ_{2} = NB A cos 18 0^{\circ} = - NB A

(∵ cos 18 0^{\circ} = - 1)

∴

Change in flux,

Δ ϕ = ϕ_{2} - ϕ_{1}

= - NB A - NB A = - 2 NB A

∣Δ ϕ ∣ = 2 NB A

Magnitude of average emf induced is

∣ ε_{a v} ∣ = \frac{∣Δ ϕ ∣}{Δ t} = \frac{2 NB A}{Δ t} = \frac{2 \times 1000 \times 2 \times 1 0 ^{- 5} \times 500 \times 1 0 ^{- 4}}{0.2}

= 10 \times 1 0^{- 3} V = 10 mV

Q. A coil has 1000 turns and 500cm2 as its area. The plane of the coil is placed perpendicular to a uniform magnetic field of 2×10−5T. The coil is rotated through 180∘ in 0.2 seconds. The average emf induced in the coil, in mV is

5

10

15

20

Q. A coil has 1000 turns and $500 c m^{2}$ as its area. The plane of the coil is placed perpendicular to a uniform magnetic field of $2 \times 1 0^{- 5} T$ . The coil is rotated through $18 0^{\circ}$ in $0.2$ seconds. The average emf induced in the coil, in $mV$ is