Q156 / 180 · COMEDK 2026 (9 May Shift 1) · Physics
A circular coil of radius 7 cm and 40 turns is rotated about its vertical diameter with an angular speed of 40 radians per second in a uniform horizontal magnetic field of $4 \times 10^{-2}\ T$. What is the maximum current induced in the coil if the resistance of the coil is $11\ \Omega$?
- A$0.9\ \text{mA}$
- B$0.09\ \text{mA}$
- C$9\ \text{mA}$
- Correct answerD$90\ \text{mA}$
Solution
Given:
Number of turns, $N = 40$
Radius of the coil, $r = 7\ \text{cm} = 0.07\ \text{m}$
Angular speed, $\omega = 40\ \text{rad/s}$
Magnetic field, $B = 4 \times 10^{-2}\ \text{T}$
Resistance, $R = 11\ \Omega$
The maximum induced emf in the coil is given by:
$\varepsilon_{max} = N B A \omega$
Substituting the area $A = \pi r^2$:
$\varepsilon_{max} = 40 \times (4 \times 10^{-2}) \times \left(\dfrac{22}{7} \times (0.07)^2\right) \times 40$
$\varepsilon_{max} = 1600 \times 4 \times 10^{-2} \times \dfrac{22}{7} \times 49 \times 10^{-4}$
$\varepsilon_{max} = 64 \times 22 \times 7 \times 10^{-4} = 0.9856\ \text{V}$
The maximum induced current is:
$I_{max} = \dfrac{\varepsilon_{max}}{R}$
$I_{max} = \dfrac{0.9856}{11} = 0.0896\ \text{A}$
$I_{max} = 89.6\ \text{mA} \approx 90\ \text{mA}$
Answer: $90\ \text{mA}$
Number of turns, $N = 40$
Radius of the coil, $r = 7\ \text{cm} = 0.07\ \text{m}$
Angular speed, $\omega = 40\ \text{rad/s}$
Magnetic field, $B = 4 \times 10^{-2}\ \text{T}$
Resistance, $R = 11\ \Omega$
The maximum induced emf in the coil is given by:
$\varepsilon_{max} = N B A \omega$
Substituting the area $A = \pi r^2$:
$\varepsilon_{max} = 40 \times (4 \times 10^{-2}) \times \left(\dfrac{22}{7} \times (0.07)^2\right) \times 40$
$\varepsilon_{max} = 1600 \times 4 \times 10^{-2} \times \dfrac{22}{7} \times 49 \times 10^{-4}$
$\varepsilon_{max} = 64 \times 22 \times 7 \times 10^{-4} = 0.9856\ \text{V}$
The maximum induced current is:
$I_{max} = \dfrac{\varepsilon_{max}}{R}$
$I_{max} = \dfrac{0.9856}{11} = 0.0896\ \text{A}$
$I_{max} = 89.6\ \text{mA} \approx 90\ \text{mA}$
Answer: $90\ \text{mA}$
Hence, the correct answer is option: 'D'.