Question

A square wire loop of $10.0\text{cm}$ side lies at right angles to a uniform magnetic field of $20\text{T}$. A $10\text{V}$ light bulb is in a series with the loop as shown in the fig. The magnetic field is decreasing steadily to zero over a time interval $\Delta t$. The bulb will shine with full brightness if $\Delta t$ is equal to

• A. $20\text{ms}$
• B. $0.02\text{ms}$
• C. $2\text{ms}$
• D. $0.2\text{ms}$

Answer 1

The correct option is A $20\text{ms}$

The bulb will shine with the full brightness when the emf induced in the loop is equal to the voltage rating of the bulb.


$\therefore$ Emf induced, $E=10\text{V}$

$\Rightarrow 10=\left|\frac{\Delta \varphi }{\Delta t}\right|=\frac{|{\varphi }_2-{\varphi }_1|}{\Delta t}$

Here, ${\varphi }_1=BA=20\times (0.1{)}^2=0.2\text{Wb}$

${\varphi }_2=0\text{Wb}[\because B=0]$

$\Rightarrow 10=\frac{|0-0.2|}{\Delta t}$

$\therefore \Delta t=\frac{0.2}{10}=0.02\text{s}=20\text{ms}$

Hence, $\left(A\right)$ is the correct answer.