Question

A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad s^-1. If the vertical component of earth’s magnetic field at that place is 2 × 10^-5 T and electrical resistance of the coil is 12.56 Ω, then the maximum induced current in the coil will be:

• A. 0.25 A
• B. 1.5 A
• C. 1 A
• D. 2 A

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
As the coil rotates in a magnetic field, the flux through it changes, inducing an alternating EMF.
The maximum EMF occurs when the rate of change of flux is highest.
Key Formula or Approach:
1. Maximum induced EMF: \(E_0 = NAB\omega\)
2. Maximum induced current: \(I_0 = \frac{E_0}{R} = \frac{NAB\omega}{R}\)
3. Area of circular coil: \(A = \pi r^2\)
Step 2: Detailed Explanation:
1. Identify given values:
Number of turns \(N = 1000\).
Radius \(r = 10 \text{ m}\). Area \(A = \pi(10)^2 = 100\pi \text{ m}^2\).
Angular speed \(\omega = 2 \text{ rad/s}\).
Magnetic field (vertical component) \(B = 2 \times 10^{-5} \text{ T}\).
Resistance \(R = 12.56 \text{ \(\Omega\)}\).
2. Calculate maximum EMF (\(E_0\)):
\[ E_0 = 1000 \times (100\pi) \times (2 \times 10^{-5}) \times 2 \]
\[ E_0 = 10^3 \times 10^2\pi \times 4 \times 10^{-5} \]
\[ E_0 = 4\pi \text{ Volts} \]
3. Calculate maximum Current (\(I_0\)):
Using \(\pi \approx 3.14\), \(4\pi \approx 4 \times 3.14 = 12.56 \text{ V}\).
\[ I_0 = \frac{E_0}{R} = \frac{4\pi}{12.56} \]
\[ I_0 = \frac{12.56}{12.56} = 1 \text{ A} \]
Step 3: Final Answer:
The maximum induced current is 1 A.