Question

A conducting ring of radius 1 meter is placed in an uniform magnetic field B of 0.01 Tesla oscillating with frequency 100 Hz with its plane at right angles to B. What will be the induced electric field:

• A. $\pi$ volts/m
• B. $2\pi$ volts/m
• C. 10 volts/m
• D. 62 volts/m

Answer 1

The correct option is B $2\pi$ volts/m

According to the question,

In the constant magnetic field conducting ring oscillates with a frequency with the frequency of the $100Hz$,

$T=\frac{1}{100}s$,

in time $\frac{T}{2}$ flux links with coil changes from $BA$ to zero induced emf $=\frac{changeinflux}{time}$

$=\frac{BA}{\frac{T}{2}}$

$=\frac{2BA}{T}$

$=\frac{2B\times \pi r^2}{T}$

$=\frac{2\times 0.01\times \pi \times 1^2}{\frac{1}{100}}$

$=4\pi V$

So, the electric field along with the circle,

Using the Maxwell equation

$\oint E.dl=-\frac{dv}{dt}$

$=A\frac{dB}{dt}$

$=e$

$E=\frac{1}{2\pi r}\times \left(\pi r^2\times \frac{dB}{dt}\right)$

$=\frac{e}{2\pi r}$

$=\frac{4\pi }{2\pi r}$

$=2Volts/m$

Hence, the induced electric field is $=2Volts/m$