First slide

Magnetic flux and induced emf

Question

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

Moderate

A

is zero
B

decreases as 1/r
C

increases as r
D

decreases as 1/r²

Solution

Construct a concentric circle of radius r. The induced electric field (E) at any point on the circle is equal to that at P.
For this circle
$\begin{array}{l} \oint \vec{E} . d \vec{l} = |\frac{d φ}{d t}| = A |\frac{d B}{d t}| \\ ⇒ E \times (2 π r) = π a^{2} \cdot |\frac{d B}{d t}| \\ \Rightarrow E = \frac{a^{2}}{2 r} |\frac{d B}{d t}| \\ \Rightarrow E \propto \frac{1}{r} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App