A conducting ring of radius r and resistance R is placed in a region of uniform time varying magnetic field B which is perpendicular to the plane of the ring. If the magnetic field is changing at a rate α , then the current induced in the ring is

Question

A conducting ring of radius r and resistance R is placed in a region of uniform time varying magnetic field B which is perpendicular to the plane of the ring. If the magnetic field is changing at a rate α , then the current induced in the ring is (A) (π r2 α /2 R) (B) (2 π r α /R) (C) ( π r α /R) (D) (π r2 α /R)

Tardigrade Admin · Accepted Answer

The magnitude of the induced emf in the ring is |ϵ |=(d φ/d t)=(d/d t)(B A)=A(d B/d t)=π r2α The induced current in the ring, I=(|ϵ |/R)=(π r2 α /R)

Q. A conducting ring of radius $r$ and resistance $R$ is placed in a region of uniform time varying magnetic field $B$ which is perpendicular to the plane of the ring. If the magnetic field is changing at a rate $α$ , then the current induced in the ring is

$\frac{π r ^{2} α}{2 R}$

$\frac{2 π r α}{R}$

$\frac{π r α}{R}$

$\frac{π r ^{2} α}{R}$

The magnitude of the induced emf in the ring is
$∣ ϵ ∣ = \frac{d ϕ}{d t} = \frac{d}{d t} (B A) = A \frac{d B}{d t} = π r^{2} α$
The induced current in the ring, $I = \frac{∣ ϵ ∣}{R} = \frac{π r ^{2} α}{R}$

Q. A conducting ring of radius r and resistance R is placed in a region of uniform time varying magnetic field B which is perpendicular to the plane of the ring. If the magnetic field is changing at a rate α , then the current induced in the ring is

2Rπr2α​

R2πrα​

Rπrα​

Rπr2α​