Question

A horizontal straight wire $10m$long extending from East to West is falling with a speed of $5.0m{s}^{-1}$ at right angles to the horizontal component of the earth's magnetic field of strength $0.30\times {10}^{-4}Wb{m}^{-2}$. What is the instantaneous value of the emf induced in the wire?

• A. $+1.5\times {10}^{-3}V{m}^{-1}$
• B. $-1.5\times {10}^{-3}V{m}^{-1}$
• C. $+1.5\times {10}^{-4}V{m}^{-1}$
• D. $-1.5\times {10}^{-4}V{m}^{-1}$

Answer 1

The correct option is A

$+1.5\times {10}^{-3}V{m}^{-1}$

Explanation for the correct option:

Step 1: Given data:

Length of the wire is $l=10m$

Velocity of the conductor, $v=5.0m{s}^{-1}$

Earth's magnetic field of strength $B=0.30\times {10}^{-4}Wb{m}^{-2}$

Step 2: Finding the instantaneous value of emf induced:

We know, $e=Blv$

putting the values of given data,

$$\begin{gathered} e=0.30\times {10}^{-4}x10x5.0 \\ =1.5\times {10}^{-3}V{m}^{-1} \end{gathered}$$

Hence, option A is correct.