Question:
A circular coil of radius 10 cm and 50 turns is rotated about its vertical diameter with an angular speed of 20 rad s\(^{-1}\) in a uniform horizontal magnetic field of magnitude \(7 \times 10^{-2}\, T\). If the closed loop resistance of the coil is 20 \(\Omega\), the maximum value of current in the coil is:
A circular coil of radius 10 cm and 50 turns is rotated about its vertical diameter with an angular speed of 20 rad s\(^{-1}\) in a uniform horizontal magnetic field of magnitude \(7 \times 10^{-2}\, T\). If the closed loop resistance of the coil is 20 \(\Omega\), the maximum value of current in the coil is:
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For rotating coil, always use peak emf formula \(N B A \omega\) to directly get maximum current.
Updated On: Jul 18, 2026
- 0.08 A
- 0.06 A
- 0.15 A
- 0.11 A
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The Correct Option is D
Solution and Explanation
Step 1: Understanding induced emf in rotating coil.
For a coil rotating in a uniform magnetic field, the induced emf is: \[ \mathcal{E} = N B A \omega \sin(\omega t) \] Hence, maximum emf is: \[ \mathcal{E}_{max} = N B A \omega \]
Step 2: Expression for maximum current.
Using Ohm’s law: \[ I_{max} = \frac{\mathcal{E}_{max}}{R} \]
Step 3: Substituting given values.
Given: \[ N = 50,\quad r = 0.1\, m,\quad B = 7 \times 10^{-2}\, T,\quad \omega = 20\, rad/s,\quad R = 20\, \Omega \] Area of coil: \[ A = \pi r^2 = \pi (0.1)^2 = 0.01\pi \]
Step 4: Compute maximum emf.
\[ \mathcal{E}_{max} = 50 \times 7 \times 10^{-2} \times 0.01\pi \times 20 \] \[ = 50 \times 0.07 \times 0.01\pi \times 20 \] \[ = 70 \times 0.01\pi = 0.7\pi \approx 2.2\, V \]
Step 5: Compute maximum current.
\[ I_{max} = \frac{2.2}{20} = 0.11\, A \]
Step 6: Final conclusion.
\[ \boxed{0.11\, A} \]
For a coil rotating in a uniform magnetic field, the induced emf is: \[ \mathcal{E} = N B A \omega \sin(\omega t) \] Hence, maximum emf is: \[ \mathcal{E}_{max} = N B A \omega \]
Step 2: Expression for maximum current.
Using Ohm’s law: \[ I_{max} = \frac{\mathcal{E}_{max}}{R} \]
Step 3: Substituting given values.
Given: \[ N = 50,\quad r = 0.1\, m,\quad B = 7 \times 10^{-2}\, T,\quad \omega = 20\, rad/s,\quad R = 20\, \Omega \] Area of coil: \[ A = \pi r^2 = \pi (0.1)^2 = 0.01\pi \]
Step 4: Compute maximum emf.
\[ \mathcal{E}_{max} = 50 \times 7 \times 10^{-2} \times 0.01\pi \times 20 \] \[ = 50 \times 0.07 \times 0.01\pi \times 20 \] \[ = 70 \times 0.01\pi = 0.7\pi \approx 2.2\, V \]
Step 5: Compute maximum current.
\[ I_{max} = \frac{2.2}{20} = 0.11\, A \]
Step 6: Final conclusion.
\[ \boxed{0.11\, A} \]
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