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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.
Solution
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"`
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