A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position M N Q, the speed of the ring is v and the potential difference developed across the ring is

Question

A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position M N Q, the speed of the ring is v and the potential difference developed across the ring is (A) zero (B) B v π R2 / 2 and M is at higher potential (C) π R B v and Q is at higher potential (D) 2 R B v and Q is at higher potential

Tardigrade Admin · Accepted Answer

Rate of decrease of area of the semicircular ring

- \frac{d A}{d t} = (2 R) v

According to Faraday's law of induction induced emf

e = - \frac{d φ}{d t} = - B \frac{d A}{d t} = - B (2 R v)

The induced current in the ring must generate magnetic field in the upward direction. Thus

Q

is at higher potential

Q. A thin semicircular conducting ring of radius $R$ is falling with its plane vertical in a horizontal magnetic induction $B$ . At the position $MNQ$ , the speed of the ring is $v$ and the potential difference developed across the ring is

zero

$B v π R^{2} /2$ and $M$ is at higher potential

$π RB v$ and $Q$ is at higher potential

$2 RB v$ and $Q$ is at higher potential

Q. A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position MNQ, the speed of the ring is v and the potential difference developed across the ring is

zero

BvπR2/2 and M is at higher potential

πRBv and Q is at higher potential

2RBv and Q is at higher potential

Rate of decrease of area of the semicircular ring −dtdA​=(2R)v According to Faraday's law of induction induced emf e=−dtdφ​=−BdtdA​=−B(2Rv) The induced current in the ring must generate magnetic field in the upward direction. Thus Q is at higher potential

Q. A thin semicircular conducting ring of radius $R$ is falling with its plane vertical in a horizontal magnetic induction $B$ . At the position $MNQ$ , the speed of the ring is $v$ and the potential difference developed across the ring is

$B v π R^{2} /2$ and $M$ is at higher potential

$π RB v$ and $Q$ is at higher potential

$2 RB v$ and $Q$ is at higher potential