A hollow dielectric sphere has $R_{1}$ and $R_{2}$ as its inner and outer radii. The total charge carried by the sphere is $+$ Q which is uniformly distributed throughout the dielectric sphere between $R_{1}$ and $R_{2}$ . The electric field for $R_{1} < r < R_{2}$ is given by :

\frac{Q}{4 π r \in R_{1}}

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\frac{Q}{4 π \in r_{2}}

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\frac{Q}{4 π \in R_{1}^{2}}

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\frac{Q (r^{3} - R_{1}^{2})}{4 π \in r^{2} (R_{2}^{3} - R_{1}^{3})}

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Solution

The correct option is D $\frac{Q (r^{3} - R_{1}^{2})}{4 π \in r^{2} (R_{2}^{3} - R_{1}^{3})}$

If $ρ$ be the volume charge density, charge $Q = ρ . \frac{4}{3} π (R_{2}^{3} - R_{1}^{3}) . . . . (1)$

Let $E$ be the electric field at $r$ . Using Gauss's law,

$E .4 π r^{2} = \frac{Q_{e n}}{ϵ}$ where $ϵ$ is the permittivity of dielectric medium.

or $E .4 π r^{2} = \frac{ρ . \frac{4}{3} π (r^{3} - R_{1}^{3})}{ϵ}$

or $E = \frac{Q (r^{3} - R_{1}^{3})}{4 π ϵ r^{2} (R_{2}^{3} - R_{1}^{3})}$ using (1)

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Similar questions

Q. A charge

q

is uniformly distributed in the hollow sphere of radii

r_{1}

and

r_{2} (r_{2} > r_{1})

. The electric field at a point

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situated at distance

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from the centre (for

r_{1} < x < r_{2}

) is :

A charge Q is distributed uniformly within the material of a hollow sphere of inner and outer radii $r_{1}$ and $r_{2}$ (figure 30-E4). Find the electric field at a point P a distance x away from the centre for $r_{1} < x < r_{2}$ . Draw a rough showing the electric field as a function of x for $0 < x < 2 r_{2}$ (figure 30-E4).