Question

A boat is moving due East in a region where the earth's magnetic field is $5.0\times {10}^{-5}N{A}^{-1}{m}^{-1}$ due North and horizontal. The boat carries a vertical aerial $2m$ long. If the speed of the boat is $1.50m{s}^{-1}$, the magnitude of the induced emf in the wire of aerial is

• A. $0.75mV$
• B. $0.50mV$
• C. $0.15mV$
• D. $1mV$

Answer 1

The correct option is C

$0.15mV$

Step 1: Given Data

Magnetic field, $B=5.0\times {10}^{-5}N{A}^{-1}{m}^{-1}$

Vertical Ariel length, $l=2m$

Velocity of boat, $v=1.50m{s}^{-1}$

Step 2: Find the induced emf

Induced emf is defined as the generation of a potential difference in a coil due to the changes in the magnetic flux through it. It is given by

$$\begin{gathered} \epsilon =Bvl \\ \epsilon =5.0\times {10}^{-5}N{A}^{-1}{m}^{-1}x1.50m{s}^{-1}x2m \\ \epsilon =15x{10}^{-5}V \\ \epsilon =0.15mV \end{gathered}$$

Hence, option C is correct.