Question

A wire $40cm$ long is bent into a rectangular frame $15cm\times 5cm$ and placed perpendicular in a magnetic field intensity of $0.8T$ . The frame is changed into a square frame and the field is increased to $1.4T$ in a time interval of $0.5s$. The e.m.f induced in the frame is ________.

• A. $1.6\times {10}^{-2}V$
• B. $1.6\times {10}^{-3}V$
• C. $1.6\times {10}^{-4}V$
• D. $1.6\times {10}^{-5}V$

Answer 1

The correct option is A $1.6\times {10}^{-2}V$

The emf induced is given by

$emf=-\frac{\Delta \left(BA\right)}{t}$

where $B$ is the magnetic field in Tesla.
$A$ is the area of the frame and $t$ is the time period.

Given:
Initial area of the frame$A_1=15\times 5=75c{m}^2$
$\begin{array}{ccc}{A}_2=a^2& |& 4a=40\\ =10\times 10& & a=10cm\\ A_2=100c{m}^2& & \end{array}$
where $A_2$ is the new area or the final area.
$e=-\frac{(B_2{A}_2-B_1{A}_1)}{t}=\frac{(1.4\times 100-0.8\times 75)\times {10}^{-4}}{0.5}$
$=-1.6\times {10}^{-2}V$