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  • A conducting ring of radius r is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is x, the electric field intensity at any

A conducting ring of radius r is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is x, the electric field intensity at any point of the ring is:

Option: 1

\mathrm{rx}


Option: 2

\mathrm{\frac{\pi x}{2}}


Option: 3

\mathrm{2 \mathrm{rx}}


Option: 4

\mathrm{\frac{4 r}{x}}


Answers (1)

Let \overrightarrow{\mathrm{E}} be the electric field intensity at a point on the circumference of the ring. Then, the emf induced \mathrm{\varepsilon=\iint \mathrm{E} \cdot \mathrm{d} \vec{l}} where dl is a length element of the ring. Since \mathrm{|\overrightarrow{\mathrm{E}}|} is constant and \mathrm{\mathrm{E} \| \mathrm{d} \vec{l}} ,

\mathrm{\varepsilon=\mathrm{E}(2 \pi \mathrm{I})} -------------(i)

Also, the induced emf is

\mathrm{\varepsilon=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\pi \mathrm{r}^2 \frac{\mathrm{dB}}{\mathrm{dt}}=\pi \mathrm{r}^2 \mathrm{x}} ------------(ii)

Equating (i) and (ii), we get

\mathrm{E=\frac{\pi x}{2}}

Posted by

Ramraj Saini

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