Question

If a magnet is plunged into a coil, then the magnitude of induced emf does not depend upon

• A. number of turns in the coil
• B. the medium of the core of the coil
• C. the insertion speed of the magnet
• D. the strength of the magnet
• E. the resistance of the coil

Hint:

Always separate: EMF → depends on flux change Current → depends on resistance

Answer 1

Answer: (E)

Concept: Faraday’s Law of Electromagnetic Induction
Whenever the magnetic flux linked with a circuit changes, an emf is induced in the circuit. Mathematically, \[ e = -\frac{d\Phi}{dt} \] For a coil of $N$ turns: \[ e = -N \frac{d\Phi}{dt} \] where:
• $e$ = induced emf
• $N$ = number of turns
• $\Phi = BA \cos\theta$ = magnetic flux ---

Step 1: Understanding magnetic flux change
When a magnet is plunged into a coil:
• Magnetic field through the coil changes with time
• Hence flux $\Phi$ changes
• This induces emf according to Faraday’s law Thus, emf depends on: \[ e \propto \frac{d\Phi}{dt} \] ---

Step 2: Expanding the expression for flux
Magnetic flux: \[ \Phi = BA \cos\theta \] Thus: \[ e = -N \frac{d(BA \cos\theta)}{dt} \] This shows emf depends on:
• Magnetic field strength ($B$)
• Area of coil ($A$)
• Orientation ($\theta$)
• Rate of change (motion of magnet)
• Number of turns ($N$) ---

Step 3: Analyze each option carefully (A) Number of turns
\[ e = -N \frac{d\Phi}{dt} \] More turns → more flux linkage → larger emf \[ \Rightarrow \text{Depends on } N \quad (\text{Important factor}) \] --- (B) Medium of core
Core material affects magnetic permeability: \[ B = \mu H \] Higher permeability → stronger magnetic field → higher flux \[ \Rightarrow \text{Affects emf} \] --- (C) Insertion speed
\[ e \propto \frac{d\Phi}{dt} \] Faster insertion → faster flux change → higher emf \[ \Rightarrow \text{Strong dependence} \] --- (D) Strength of magnet
Stronger magnet → larger magnetic field $B$ → larger flux \[ \Rightarrow \text{Higher emf} \] --- (E) Resistance of coil
This is the key point. From Faraday’s law: \[ e = -N \frac{d\Phi}{dt} \] No resistance term appears. Resistance only affects current: \[ I = \frac{e}{R} \] Important distinction:
• EMF depends on flux change
• Current depends on resistance Thus: \[ \boxed{\text{EMF is independent of resistance}} \] ---

Step 4: Physical Interpretation

• EMF is generated due to changing magnetic environment
• Resistance only determines how much current flows AFTER emf is produced
• Even with very large resistance, emf is still induced --- Final Conclusion: \[ \boxed{\text{The induced emf does not depend on resistance of the coil}} \]