Question

A magnetic flux of $5.5\times {10}^{-4}\text{Wb}$ is linked with a coil of resistance $10\Omega$ and $1\text{turn}$. If the magnetic flux is changed to $5\times {10}^{-4}\text{Wb}$ in $0.1\text{sec}$, the induced charge in the coil is,

• A. $50\mu \text{C}$
• B. $5\mu \text{C}$
• C. $2\mu \text{C}$
• D. $20\mu \text{C}$

Answer 1

The correct option is B $5\mu \text{C}$

Given,

Resistance of coil, $R=10\Omega$

Number of turns, $N$ = $1$

${\varphi }_1=5.5\times {10}^{-4}\text{Wb}$

${\varphi }_2=5\times {10}^{-4}\text{Wb}$

$\Delta t=0.1\text{sec}$

Change in flux, $|\Delta \varphi |=|{\varphi }_2-{\varphi }_1|$

$|\Delta \varphi |=|5\times {10}^{-4}-5.5\times {10}^{-4}|=0.5\times {10}^{-4}$

The charge flown through the circuit is given by,

$q=\frac{\Delta \varphi }{R}=\frac{0.5\times {10}^{-4}}{10}=5\mu \text{C}$

Hence, option ($B$) is the correct answer.

Why this Question? Note: To solve this question, we did not use the time interval $0.1\text{sec}$. Instead we directly used the expression, $q=\frac{\Delta \varphi }{R}$