Question

A wire loop that encloses an area of $20c{m}^2$ has a resistance of $10\Omega$. The loop is placed in a magnetic field of $2.4T$ with its plane perpendicular to the field. The loop is suddenly removed from the field. How much charge flows past a given point in the wire?

• A. $12\times {10}^{-4}C$
• B. ${10}^{-1}C$
• C. $4.8\times {10}^{-4}C$
• D. $2.4\times {10}^{-3}C$

Answer 1

Answer: (C)

$4.8\times {10}^{-4}C$

Given,
Resistance, $R=10\Omega$
Area of the loop, $A=20c{m}^2=20\times {10}^{-4}{m}^2$
Magnetic field, $B=2.4T$
As we know, induced $emf|e|=+\frac{d\varphi }{dt}\Rightarrow IR\frac{d\varphi }{dt}$
$\Rightarrow \frac{dQ}{dt}.R=\frac{d\varphi }{dt}\Rightarrow \int dQ=\int \frac{d\varphi }{R}$
$\Rightarrow Q=\frac{\varphi }{R}[\because \varphi =BA\cos 0^{\circ }=BA]$
$=\frac{(20\times {10}^{-4})\left(2.4\right)}{10}$
$=4.8\times {10}^{-4}C$