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Standard XII

Physics

Superposition of Electric Fields

A solid insul...

Question

A solid insulating sphere of radius $5 c m$ carries electric charge uniformly distributed throughout its volume.Concentric with the sphere is a conducting spherical shell with no net charge as shown in Figure O Q24.9. The inner radius of the shell is $10 c m$ , and the outer radius is $15 c m$ . No other charges are nearby. Rank the magnitude of the electric field at points $A$ (at radius
$4 c m$ ), $B$ (radius $8 c m$ ), $C$ (radius $12 c m$ ), and $D$ (radius $16 c m$ ) from largest to smallest.Display any cases of equality in your ranking.

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Solution

The ranking is $A > B > D > C$ . Let $q$ represent the charge of the insulating sphere The field at $A$ is $(4 / 5)^{3} q / [4 π (4 c m)^{2} ϵ_{0}]$ . The field at $B$ is $q / [4 π (8 c m)^{2} ϵ_{0}]$ . The field at $C$ is zero. The field at $D$ is $q / [4 π (16 c m)^{2} ϵ_{0}]$

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The ranking is A>B>D>C. Let q represent the charge of the insulating sphere The field at A is (4/5)3q/[4π(4cm)2ϵ0]. The field at B is q/[4π(8cm)2ϵ0]. The field at C is zero. The field at D is q/[4π(16cm)2ϵ0]

The ranking is $A > B > D > C$ . Let $q$ represent the charge of the insulating sphere The field at $A$ is $(4 / 5)^{3} q / [4 π (4 c m)^{2} ϵ_{0}]$ . The field at $B$ is $q / [4 π (8 c m)^{2} ϵ_{0}]$ . The field at $C$ is zero. The field at $D$ is $q / [4 π (16 c m)^{2} ϵ_{0}]$