Question

A wire loop that encloses an area of $20\, cm^2$ has a resistance of $10Ω$. The loop is placed in a magnetic field of $2.4\, T$ 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. $4.8 × 10^{- 4}C$
• B. $2.4 × 10^{- 3}C$
• C. $1.2 × 10^{- 4}C$
• D. $10 ^{- 1}C$

Answer 1

Answer: (A)

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