Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

A wheel with 20 metallic spokes, each 1 m long, is rotated with a speed of 120 rpm in a plane perpendicular to a magnetic field of 0.4 G. The induced emf between the axle and rim of the wheel will be: (1 G = 10⁻⁴ T)

2.51 × 10⁻⁴ V

2.51 × 10⁻⁵ V

4.0 × 10⁻⁵ V

2.51 V

Step-by-Step Solution

Formula: The induced electromotive force (emf) $\varepsilon$ between the center (axle) and the rim of a rotating rod (spoke) is given by $\varepsilon = \frac{1}{2} B \omega R^2$ , where $B$ is the magnetic field, $\omega$ is the angular velocity, and $R$ is the length of the spoke .
Parallel Combination: Although there are 20 spokes, they are all connected in parallel between the axle and the rim. In a parallel combination of identical cells (spokes), the equivalent emf is equal to the emf of a single cell. Therefore, the number of spokes does not affect the magnitude of the induced voltage .
Unit Conversions: Magnetic Field ( $B$ ): $0.4 \text{ G} = 0.4 \times 10^{-4} \text{ T}$ . Angular Velocity ( $\omega$ ): $120 \text{ rpm} = \frac{120 \times 2\pi}{60} \text{ rad/s} = 4\pi \text{ rad/s}$ .

Length ( $R$ ): $1 \text{ m}$ .

Calculation: $\varepsilon = \frac{1}{2} \times (0.4 \times 10^{-4}) \times (4\pi) \times (1)^2$ $\varepsilon = 0.2 \times 10^{-4} \times 4 \times 3.14$ $\varepsilon = 0.8 \times 3.14 \times 10^{-4}$ $\varepsilon \approx 2.512 \times 10^{-4} \text{ V}$ .

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