The Question is from neet-physics , and it was created by the author SUBHANI

Question

The magnitude of the induced emf in a coil rotating in a magnetic field does NOT depend on:

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: D
## CONCEPT FRAMEWORK
 **Primary Concept**: Faraday's Law of Induction and its application to rotating coils.
 **Related Topics**: Electromagnetic induction, magnetic flux, angular velocity.
 **Prerequisites**: Understanding of magnetic fields, induced emf, and basic calculus (derivatives).
## SOLUTION PATHWAY
**Given Information**:
A coil rotating in a uniform magnetic field.
**Method & Steps**:
The magnitude of the induced emf ($\epsilon$) in a coil rotating in a magnetic field is given by Faraday's Law of Induction:
1. Understanding Faraday's Law:
  Reasoning: The induced emf is proportional to the rate of change of magnetic flux through the coil.  When a coil rotates in a magnetic field, the magnetic flux through the coil changes periodically.
  Formula/Rule: $\epsilon = -N \frac{d\Phi}{dt}$, where $N$ is the number of turns, and $\Phi$ is the magnetic flux.
2. Analyzing Magnetic Flux:
  Working: The magnetic flux through the coil is given by $\Phi = BAcos(\omega t)$, where $B$ is the magnetic field strength, $A$ is the area of the coil, and $\omega$ is the angular speed. Substituting this into Faraday's Law and taking the derivative with respect to time, we get:
$ \epsilon = N B A \omega sin(\omega t) $
  Key Point: The magnitude of the induced emf is proportional to $N$, $B$, $A$, and $\omega$.
3. Identifying Independent Variable:
  Result: The resistance of the coil ($R$) does not appear in the equation for the induced emf.  The induced emf is determined by the coil's geometry, the magnetic field, and the rotation speed, not its resistance.
  Verification: The resistance only affects the current that flows in the coil due to the induced emf (Ohm's Law: $I = \frac{\epsilon}{R}$), not the emf itself.
 ## OPTION ANALYSIS
A ✓: The number of turns ($N$) directly affects the induced emf.
B :x: The area of the coil ($A$) directly affects the induced emf.
C :x: The angular speed ($\omega$) directly affects the induced emf.
D :x: The resistance of the coil ($R$) does NOT affect the induced emf, only the resulting current.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing induced emf with induced current:  The resistance affects the current, not the emf.
  2.Ignoring the angular dependence: The emf is not constant but varies sinusoidally with time.
 **Quick Tips**:
  1.Remember the formula for induced emf in a rotating coil to quickly identify the factors.
  2.Focus on the rate of change of magnetic flux as the key to understanding Faraday's Law.

SUBHANI · Answer

The number of turns in the coil.

SUBHANI · Answer

The area of the coil.

SUBHANI · Answer

The angular speed of rotation.

SUBHANI · Answer

The correct Option is "The resistance of the coil."

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