Identify the correct statements among the following:
A. Induced emf in a coil of \( N \) turns, when magnetic flux \( (\Phi_B) \) through it is changing with time \( \displaystyle = -N\frac{d\Phi_B}{dt} \)
B. Motional emf across the ends of a rod of length \( l \) moving with velocity \( v \) perpendicular to a uniform magnetic field \( B \), \( = Blv \)
C. emf generated in a coil due to mutual induction, when there is a changing current \( I_2 \) in an adjacent coil \( \displaystyle = -M_{12}\frac{dI_2}{dt} \)
D. emf generated in a coil due to self induction when the current in it is changing, \( \displaystyle = -L\frac{dI}{dt} \)
E. Maximum induced emf in a coil of \( N \) turns and area \( A \), rotating with the angular frequency \( \omega \) in a uniform magnetic field \( B \), \( = NBA\omega \).
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A, B, C, D and E
Each statement is a standard expression of electromagnetic induction.
(A) Induced emf in a coil of \( N \) turns, when magnetic flux \( (\Phi_B) \) through it is changing with time \( \displaystyle = -N\frac{d\Phi_B}{dt} \) — Correct. This is Faraday’s law.
(B) Motional emf across the ends of a rod of length \( l \) moving with velocity \( v \) perpendicular to a uniform magnetic field \( B \), \( = Blv \) — Correct. The flux cut per second is \( Blv \).
(C) emf generated in a coil due to mutual induction, when there is a changing current \( I_2 \) in an adjacent coil \( \displaystyle = -M_{12}\frac{dI_2}{dt} \) — Correct. The flux in coil 1 is \( M_{12}I_2 \) (mutual induction).
(D) emf generated in a coil due to self induction when the current in it is changing, \( \displaystyle = -L\frac{dI}{dt} \) — Correct. The flux linkage is \( LI \).
(E) Maximum induced emf in a coil of \( N \) turns and area \( A \), rotating with the angular frequency \( \omega \) in a uniform magnetic field \( B \), \( = NBA\omega \) — Correct. The emf is \( NBA\omega\sin\omega t \), whose peak is \( NBA\omega \).