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  • 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 a

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

Option: 1

is zero


Option: 2

decreases as 1/r


Option: 3

increases as r


Option: 4

decreases as 1/r^{2}


Answers (1)

best_answer


\mathrm{\mid\left\{\vec{E} \cdot \vec{d} l \quad=\left|\frac{d \phi}{d t}\right|\right. =S\left|\frac{d B}{d t}\right| }
or
\mathrm{E(2 \pi r)=\pi a^2\left|\frac{d B}{d t}\right| for r \geq \therefore \quad E=\frac{a^2}{2 r}\left|\frac{d B}{d t}\right| \therefore Induced\, electric \, \, field \propto \frac{1}{r} For \quad r \leq a }
\mathrm{E(2 \pi r)=\pi r^2\left|\frac{d B}{d t}\right| }
or
\mathrm{E=\frac{r}{2}\left|\frac{d B}{d t}\right| or E \propto r At r=a, E=\frac{a}{2}\left|\frac{d B}{d t}\right| }
Therefore, variation of E with r (distance from center) will be as follows :

Posted by

Nehul

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