Question

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

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

Answer 1

Answer: (D)

Induced emf $=\frac{N \Delta \phi}{\Delta t}$
Peak value $=N_{1} B A_{1} \omega=100 V$
Here, $2 \pi r_{1} \times 100=2 \pi r_{2} \times N_{2}$(given)
$N_{2} =\frac{r_{1} \times 100}{r_{2}}=\frac{1 \times 100}{2}=50=\frac{N_{1}}{2}$
$\because e_{0} =N_{2} B A_{2} \omega$
$\Rightarrow e_{0} =\frac{N}{2} \times B \times 4 A_{1} \times \omega$
$=2 \times(\text { initial emf} )=200 V $
$\left(\because A_{2}=4 A_{1}\right)$