A uniform but time varying magnetic field B(t) exists in a circular region of radius R and directed into the plane of paper. The magnitude of induced electric field at a point P at a distance r (r R) from the centre of the circular region is proportional to

Question

A uniform but time varying magnetic field B(t) exists in a circular region of radius R and directed into the plane of paper. The magnitude of induced electric field at a point P at a distance r (r > R) from the centre of the circular region is proportional to (A) r2 (B) (1/r) (C) (1/r2) (D) r

Tardigrade Admin · Accepted Answer

-∫ E.dl = -(dφ/dt) E.2π r=π R2.(dB/dt) E = (R2/2r).(dB/dt) ⇒ E propto(1/r)

Q. A uniform but time varying magnetic field B(t) exists in a circular region of radius R and directed into the plane of paper. The magnitude of induced electric field at a point P at a distance r (r > R) from the centre of the circular region is proportional to

$r^{2}$

$\frac{1}{r}$

$\frac{1}{r ^{2}}$

$r$

$- \int E . d l = - \frac{d ϕ}{d t}$
$E .2 π r = π R^{2} . \frac{d B}{d t}$
$E = \frac{R ^{2}}{2 r} . \frac{d B}{d t}$
$\Rightarrow E \propto \frac{1}{r}$

Q. A uniform but time varying magnetic field B(t) exists in a circular region of radius R and directed into the plane of paper. The magnitude of induced electric field at a point P at a distance r (r > R) from the centre of the circular region is proportional to

r2

r1​

r21​

r

−∫E.dl=−dtdϕ​ E.2πr=πR2.dtdB​ E=2rR2​.dtdB​ ⇒E∝r1​

$r^{2}$

$\frac{1}{r}$

$\frac{1}{r ^{2}}$

$r$

$- \int E . d l = - \frac{d ϕ}{d t}$
$E .2 π r = π R^{2} . \frac{d B}{d t}$
$E = \frac{R ^{2}}{2 r} . \frac{d B}{d t}$
$\Rightarrow E \propto \frac{1}{r}$