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. $4.8\times 10^{-4}C$
• B. $2.4\times 10^{-3}C$
• C. $1.2\times 10^{-4}C$
• D. $10^{-1}C$

Answer 1

Answer: (A)

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 $|e|=+\frac{d\varphi }{dt}$
$\Rightarrow IR=\frac{d\varphi }{dt}$
$\Rightarrow \frac{dQ}{dt}\cdot R=\frac{d\varphi }{dt}$
$\Rightarrow \int dQ=\int \frac{d\varphi }{R}$
$\Rightarrow Q=\frac{\varphi }{R}$
$\left[\because \varphi =BA\cos 0^{\circ }=BA\right]$
$=\frac{\left(20\times 10^{-4}\right)(2.4)}{10}$
$=4.8\times 10^{-4}C$