Question

a circular ring of radius 1 m is placed in a time varying magnetic field ,dB/dt=2T/s. The potential difference between P and Q is , where

Answer 1

Solution :

⏭ Given:

✏ Radius of ring = 1m

✏ Time varying magnetic field is given as dB/dt = 2 T/s

⏭ To Find:

✏ Potential difference across the ring

⏭ Formula:

✏ As per faraday's law of inducing EMF

$\star \: \underline{ \boxed{ \bold{ \sf{ \pink{p.d. = \frac{d(BA)}{dt}}}}}} \: \star$

⏭ Terms indication:

✏ B denotes magnetic field

✏ A denotes area

✏ t denotes time

⏭ Calculation:

$\implies \sf \: p.d. = \frac{d(BA)}{dt} = A \frac{dB}{dt} \: ( \because \: Area = constant) \\ \\ \implies \sf \: p.d. = \pi {r}^{2} \frac{dB}{dt} = \pi {(1)}^{2} \times 2 = 2\pi \\ \\ \implies \underline{ \boxed{ \bold{ \sf{ \purple{p.d. = 6.28 \: V}}}}} \: \orange{ \bigstar}$