Question

A 0⋅5 m long solenoid of 10 turns/cm has the area of cross-section 1 cm². Calculate the voltage induced across its ends if the current in the solenoid is changed from 1 A to A in 0⋅1 s.

Answer 1

Length of the solenoid = 0.5 m
Area if cross-section = 1 cm²
Number of turns per unit centimeter of length = 10
Total number of turns = 500

When the current in the solenoid is changed an emf is induced in the coil due to the self-induction of the solenoid.

Self-inductance of a solenoid, `"L" = (mu_@"N"^2"A")/"l"`

`"L" = (4pixx10^-7xx(500)^2xx1xx10^-4)/0.5 = 6.28 xx 10^-5 "H"`

Magnetic Flux linked with the solenoid, Φ = LI

dΦ= LdI

⇒ dΦ = 6.28 × 10^-5 × (2 Amp - 1 Amp)

⇒ dΦ= 6.28 × 10^-5 Weber

Change in magnetic flux, dΦ= 6.28 × 10^-5 Weber

Induced emf, e `=("d"phi)/"dt"`

`"e" = -(6.28xx10^-5)/0.1 = 6.28 xx 10^-4 "V"`