A circular ring of radius r is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B=K t, where K is a constant and t is the time. The electric field in the ring is

Question

A circular ring of radius r is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B=K t, where K is a constant and t is the time. The electric field in the ring is (A) (K r/4) (B) (K r/3) (C) (K r/2) (D) (K/2 r)

Tardigrade Admin · Accepted Answer

oint vecE d vecl=(d φB/d t) or E 2 π r=(d/d t)(K t × π r2) or E=(K r/2)

Q. A circular ring of radius $r$ is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field $B$ changes with time according to the equation $B = K t$ , where $K$ is a constant and $t$ is the time. The electric field in the ring is

$\frac{Kr}{4}$

$\frac{Kr}{3}$

$\frac{Kr}{2}$

$\frac{K}{2 r}$

$\oint E d l = \frac{d ϕ _{B}}{d t}$
or $E 2 π r = \frac{d}{d t} (K t \times π r^{2})$
or $E = \frac{Kr}{2}$

Q. A circular ring of radius r is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B=Kt, where K is a constant and t is the time. The electric field in the ring is

4Kr​

3Kr​

2Kr​

2rK​