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The magnetic field at all points within the cylindrical region whose cross-section is indicated in the accompanying figure start increasing at a constant rate $α T / s$ . Find the magnitude of electric field as a function of , the distance from the geometric centre of the region.

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By Expert Faculty of Sri Chaitanya

f o r r \leq R, E = \frac{r α}{2}; f o r r \geq R, E = \frac{α R^{2}}{2 r}

f o r r \leq R, E = \frac{α}{2}; f o r r \geq R, E = \frac{α R^{2}}{r}

f o r r \leq R, E = \frac{α}{2}; f o r r \geq R, E = \frac{R^{2}}{2 r}

f o r r \leq R, E = \frac{r}{2}; f o r r \geq R, E = \frac{α}{2 r}

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detailed solution

Correct option is A

For $r \leq R$

Using $E l = S |\frac{d B}{d t}|$ or $E (2 πr) = ({πr}^{2}) α$

The magnetic field at all points within the cyllindrical region whose cross section is indicated in the accompanying Figure starts increasing at a constant rate alpha. T//s. find the magnitud of electric

$E = \frac{r α}{2}$

$E \propto r$ , i.e. E-r graph is a straight line passing through origin.

At $r = R$ , $E = \frac{R α}{2}$

For $r \geq R$

Using $E l = S |\frac{d B}{d t}|$ ,

$E (2 πr) = (π R^{2}) α E = \frac{α R^{2}}{2 r}$

$E \propto \frac{1}{r}$ , i.e. E-r graph is a rectangular hyperbola.

The E-r graph is as shown in figure.

The direction of electric field is shown in above figure.

moderate

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The magnetic field at all points within the cylindrical region whose cross-section is indicated in the accompanying figure start increasing at a constant rate α T/s. Find the magnitude of electric field as a function of , the distance from the geometric centre of the region.

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The magnetic field at all points within the cylindrical region whose cross-section is indicated in the accompanying figure start increasing at a constant rate $α T / s$ . Find the magnitude of electric field as a function of , the distance from the geometric centre of the region.