Question

When a circular coil of radius $1m$ and $100$ turns is rotated in a horizontal uniform magnetic field, the peak value of emf induced is $100V$. The coil is unwound and then rewound into a circular coil of radius $2m$. If it is rotated now, with the same speed, under similar conditions, the new peak value of emf developed is

• A. $50V$
• B. $25V$
• C. $100V$
• D. $200V$

Answer 1

Answer: (D)

Induced emf $=\frac{N\Delta \varphi }{\Delta t}$
Peak value $=N_{1}B{A}_1\omega =100V$
Here, $2\pi r_1\times 100=2\pi r_2\times N_2$(given)
$N_2=\frac{r_1\times 100}{r_2}=\frac{1\times 100}{2}=50=\frac{N_1}{2}$
$\because e_0=N_{2}B{A}_2\omega$
$\Rightarrow e_0=\frac{N}{2}\times B\times 4A_1\times \omega$
$=2\times (\text{ initial emf})=200V$
$\left(\because A_2=4A_1\right)$