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Question

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the center of the shell?


A

F=14πε0qQR2>F>0forr<R

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B

F=14πε0qQr2forr>R

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C

F=14πε0qQr2forallr

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D

F=14πε0qQR2forr<R

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Solution

The correct option is B

F=14πε0qQr2forr>R


Step 1. Finding the Electric field E at r<R.

Consider a gaussian surface of radius r inside the Spherical shell of radius R

Using the integral form of the gauss law of electrostatic

E.ds=Qenε0, [Where Qenis the enclosed charge and ε0 is the permittivity of the free space, and ds is the area enclosed.]

In this case,

Qen=0

E.ds=0

E=0

Step 2. Finding the electric field E at r>R

Consider a gaussian surface of radius r outside the spherical shell of radius R

Using an integral form of gauss law

E.ds=Qenε0

Eds=Qε0

E4πr2=Qε0 [Surface area of the sphere=4πr2]

E=Q4πε0r2

Step 3. Finding the Force, F

We know that, F=qE

F=14πε0qQr2

Hence the correct option is B.


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