Question

A horizontal straight wire 5 m long, extending from east to west, is falling freely at a right angle to the horizontal component of Earth's magnetic field \( 0.60 \times 10^{-4} \, \text{Wb/m}^2 \). The instantaneous value of emf induced in the wire when its velocity is \( 10 \, \text{m/s} \) is _______ \( \times 10^{-3} \, \text{V} \).

Answer 1

Correct Answer: 3

To determine the instantaneous emf induced in the wire, we use the formula for motional emf: \( \text{emf} = B \cdot l \cdot v \), where \( B \) is the magnetic field strength, \( l \) is the length of the wire, and \( v \) is the velocity of the wire.
Given:

• \( B = 0.60 \times 10^{-4} \, \text{Wb/m}^2 \)
• \( l = 5 \, \text{m} \)
• \( v = 10 \, \text{m/s} \)

Substitute these values into the formula:

\(\text{emf} = (0.60 \times 10^{-4}) \times 5 \times 10 = 0.60 \times 10^{-3} \, \text{V}\)

This value of \( 0.60 \times 10^{-3} \, \text{V} \) falls within the provided range of 3 to 3. Thus, the correct answer is 0.60 when expressed in units of \( \times 10^{-3} \, \text{V} \). Therefore, the induced emf in the wire is \( 0.60 \times 10^{-3} \, \text{V} \).