A coil of area 50 cm² has 1000 turns. Magnetic field of 0.2 weber/m² is perpendicular to the coil. The magnetic field is reduced to zero in 0.2 second. The induced emf in the coil is.

CONCEPT:

Faraday's first law of electromagnetic induction:

• Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced.
• If the conductor circuit is closed, a current is induced which is called induced current.

​Faraday's second law of electromagnetic induction:

• The induced emf in a coil is equal to the rate of change of flux linked with the coil.

\(⇒ e=-N\frac{dϕ}{dt}\)

Where N = number of turns, dϕ = change in magnetic flux and e = induced e.m.f.

• The negative sign says that it opposes the change in magnetic flux which is explained by Lenz law.

CALCULATION:

Given θ = 0, A = 50 cm2, N = 1000, B₁ = 0.2 weber/m2, B2 = 0 weber/m2, and dt = 0.2 sec

⇒ A = 50 cm2 = 50 × 10-4 m2

• The change in the magnetic field is given as,

⇒ dB = B₂ - B₁

⇒ dB = 0 - 0.2

⇒ dB = - 0.2 weber/m2

• When the magnetic field is changing and the area remains constant, the magnetic flux is given as,

⇒ dϕ = A.dB.cosθ

⇒ dϕ = A.dB.cos0

⇒ dϕ = A.dB

⇒ dϕ = -50 × 10-4 × 0.2

⇒ dϕ = -10 × 10-4 

⇒ dϕ = 10-3 weber     -----(1)

• By Faraday's law of electromagnetic induction, the magnitude of the induced emf in the coil is given as,

\(⇒ e=-N\frac{dϕ}{dt}\)

\(⇒ e=-1000\times\frac{-10^{-3}}{0.2}\)

⇒ e =  5 V

• Hence, option 2 is correct.