Question

A long solenoid having 400 turns per cm carries a current 2A. A 100 turn coil of cross-sectional area 4 cm² is placed co-axially inside the solenoid so that the coil is in the field produced by the solenoid. Find the emf induced in the coil if the current through the solenoid reverses its direction in 0.04 sec.

Answer 1

Given data:

n₁ = 400 turns/cm

∴ n₁ = 4000 turns/m

n₂ = 100

A₂ = 4 × 10^-4 m²

i = 1 m

di = 2-(-2) = 48

dt = 0.04 sec

induced emf ε = ${\displaystyle \frac{\text{Mdi}}{\text{dt}}}$

${\displaystyle \therefore \epsilon ={\mu }_0{\text{n}}_2{\text{n}}_2{\text{A}}_{2}l\times \frac{\text{di}}{\text{dt}}}$

ε = ${\displaystyle \frac{4\pi \times 106-7\times 40000\times 100\times 4\times 106-4\times 1\times 4}{0.04}}$

${\displaystyle =\frac{64\pi \times 106-5\times 4}{4\times {10}^{-2}}}$

= 64π × 10^-3 V

= 200.96 × 10^-3 V

= 0.20 V