Question

According to Faraday's law, the induced E.M.F generated in a closed loop is equal to the \dots

• A. magnetic flux passing through it.
• B. change of magnetic flux passing through it.
• C. rate of change of magnetic flux passing through it.
• D. cross sectional area of the loop.

Hint:

A constant magnetic field cannot induce current. Only changing magnetic flux can produce induced E.M.F. Faster change means greater induced voltage.

Answer 1

The Correct Option is C

Concept: Faraday’s Law of Electromagnetic Induction states that whenever the magnetic flux linked with a closed circuit changes, an electromotive force (E.M.F.) is induced in the circuit. The magnitude of the induced E.M.F. depends on how rapidly the magnetic flux changes with time.

Step 1: Recall Faraday’s law formula. \[ \varepsilon = -\frac{d\Phi_B}{dt} \] where:
• $\varepsilon$ = induced electromotive force
• $\Phi_B$ = magnetic flux
• $\frac{d\Phi_B}{dt}$ = rate of change of magnetic flux

Step 2: Understand the meaning of the formula. The formula clearly shows that induced E.M.F. depends not on the magnetic flux itself, but on how quickly the flux changes with time. If the magnetic flux remains constant, then: \[ \frac{d\Phi_B}{dt} = 0 \] and therefore no induced E.M.F. is produced.

Step 3: Identify the correct option. Faraday’s law states that induced E.M.F. is equal to the: \[ \boxed{\text{rate of change of magnetic flux}} \] Hence, the correct answer is option (3).