Question

A train with an axle of length 1.66 m is moving towards north with a speed of 90 km/h. If the vertical component of the earth’s magnetic field is \( 0.2 \times 10^{-4} \) T, the emf induced across the ends of the axle is:

• A. \( 16.6 \) mV
• B. \( 1.66 \) mV
• C. \( 0.83 \) mV
• D. \( 8.3 \) mV

Hint:

The induced emf in a moving conductor is given by \( \mathcal{E} = B L v \).
- Always convert speed to m/s before substitution.

Answer 1

The Correct Option is C

The emf induced across the ends of a moving conductor in a magnetic field is given by: \[ \mathcal{E} = B L v \] where: - \( B = 0.2 \times 10^{-4} \) T (magnetic field), - \( L = 1.66 \) m (length of the axle), - \( v = 90 \) km/h \( = \frac{90 \times 1000}{3600} = 25 \) m/s. 1. Substituting values: \[ \mathcal{E} = (0.2 \times 10^{-4}) \times 1.66 \times 25 \] \[ = (0.2 \times 1.66 \times 25) \times 10^{-4} \] \[ = (8.3) \times 10^{-4} \text{ V} \] \[ = 0.83 \text{ mV} \] Thus, the correct answer is \(\boxed{0.83 \text{ mV}}\).