A thin semicircular conducting ring (PQR) of radius is falling with its plane vertical in a horizontal magnetic field , as shown in the figure. The potential difference developed across the ring when its speed is , is [2014]

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Q.
A thin semicircular conducting ring (PQR) of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B$ , as shown in the figure. The potential difference developed across the ring when its speed is $v$ , is [2014]

1 zero

2 $\frac{B v π r^{2}}{2}$ and $P$ is at higher potential

3 $π r B v$ and $R$ is at higher potential

4 $2 r B v$ and $R$ is at higher potential

Ans.
(4)

Motional emf induced in the semicircular ring PQR is equivalent to the motional emf induced in the imaginary conductor PR.

i.e., $ε_{P Q R} = ε_{P R} = B v l = B v (2 r)$ $(l = P R = 2 r)$

Therefore, potential difference developed across the ring is $2 r B v$ with $R$ at higher potential.

Solution

Q.
A thin semicircular conducting ring (PQR) of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B$ , as shown in the figure. The potential difference developed across the ring when its speed is $v$ , is [2014]

1 zero

2 $\frac{B v π r^{2}}{2}$ and $P$ is at higher potential

3 $π r B v$ and $R$ is at higher potential

4 $2 r B v$ and $R$ is at higher potential

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Solution

Q. A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in the figure. The potential difference developed across the ring when its speed is v, is [2014]

1 zero

2 Bvπr22 and P is at higher potential

3 πrBv and R is at higher potential

4 2rBv and R is at higher potential

Ans. (4) Motional emf induced in the semicircular ring PQR is equivalent to the motional emf induced in the imaginary conductor PR. i.e., εPQR=εPR=Bvl=Bv(2r) (l=PR=2r) Therefore, potential difference developed across the ring is 2rBv with R at higher potential.

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Q.
A thin semicircular conducting ring (PQR) of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B$ , as shown in the figure. The potential difference developed across the ring when its speed is $v$ , is [2014]

2 $\frac{B v π r^{2}}{2}$ and $P$ is at higher potential

3 $π r B v$ and $R$ is at higher potential

4 $2 r B v$ and $R$ is at higher potential