A conducting ring of radius 1m is placed in a uniform magnetic...

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

i.e.,~$\text{T} = \dfrac{1}{100}\text{s}$,~in time $\dfrac{\text{T}}{2}$

~

to zero.

$⇒$~Induced emf $= \dfrac{\text{change in flux}}{\text{time}}$

$= \dfrac{BA}{T / 2} = \dfrac{2BA}{T} = \dfrac{2B \times \pir^{2}}{T} = \dfrac{2 \times 0 .01 \times \pi \times {1}^{2}}{1 / 100} = 4\pi volts$

The induced electric field along the circle, using Maxwell equation, is,$∮ \overset{→}{E} \cdot d\overset{→}{l} = - \dfrac{dϕ}{dt} = A\dfrac{dB}{dt} = e$

$⇒ E = \dfrac{1}{2\pir} \times \left(\pir^{2} \times \dfrac{\text{d}B}{\text{d}t}\right) = \dfrac{e}{2\pir} = \dfrac{4\pi}{2\pir} = 2Vm^{- 1}$