2019 Electric Charges and FieldsGauss's Law – Field of a Uniformly Charged Spherical Shell Easy Question 15 of 42 in Electric Charges and Fields

A hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at a distance $r$ from the centre:

A increases as $r$ increases for $rR$
B zero as $r$ increases for $rR$
C zero as $r$ increases for $rR$
D decreases as $r$ increases for $rR$

The answer is B.

Solution

The charge $Q$ is distributed over the surface of the hollow metal sphere. (i) For $rR$ (outside): $q_{en}=Q$, so $E_0\cdot4\pi r^2=\frac{Q}{\epsilon_0}\Rightarrow E_0=\frac{Q}{4\pi\epsilon_0r^2}\propto\frac{1}{r^2}$ So the field is zero for $rR$.

Concept field of a hollow charged sphere

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42 questions from this chapter have appeared across 23 exam years.