Question

A conducting coil of 50 turns and area `5/pi` cm² is rotating along the axis of a solenoid of length 50 cm and 2000 turns, carrying a current of 5 A. What will be the value of the maximum emf generated?

Answer 1

Given: Turns on rotating coil (N_c) = 50

Area of coil (A) = `5/pi` cm² = `5/pi xx 10^-4 m^2`

For solenoid:

Total turns (N_s) = 2000

Length (L) = 0.5 m

Turns per metre (n) = `N_s/L`

= `2000/0.5`

= 4000 turns/m

Current in solenoid (I) = 5 A

μ₀ ​= 4π × 10⁻⁷ H/m

1. Magnetic field inside solenoid:

B = μ₀nI

= 4π × 10⁻⁷ × 4000 × 5

= 20000 × 4π × 10⁻⁷

= 2 × 10⁴ × 4π × 10⁻⁷

= 8π × 10⁻³ T

2. Flux linked with rotating coil:

Φ_B = N_cBA cos ωt

= `50 xx (8 pi xx 10^-3) xx (5/pi xx 10^-4) cos ωt`

= 50 × 8 × 10⁻³ × 5 × 10⁻⁴ cos ωt

= 2000 × 10⁻⁷ cos ωt

= 2 × 10⁻⁴ cos (ωt) Wb

3. Induced emf:

ε = `(-dΦ_"B")/(dt)`

= `-d/dt(2 xx 10^-4 cos ωt)`

= 2 × 10⁻⁴ ω sin (ωt)

sin ωt = 1

ε_max = 2 × 10⁻⁴ ωV