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Question

The equipotential surfaces corresponding to a single positive charge are concentric spherical shells with the charge at its origin. The spacing between the surfaces for the same change in potential:


A
is uniform throughout the field
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B
is getting closer as r
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C
is getting closer as r0
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D
can be varied as one wishes to
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Solution

The correct option is D is getting closer as r0
Let the equipotential surfaces have potential V1,V2,V3with,V1>V2>V3
Also, let V3V2=V2V1=R
Potential of a charge is given by kQ/r
V=kQ/rr=kQ/V
Distance between the equipotential surfaces is
kQ(1V21V3) and kQ(1V11V2)
or
kQ(V3V2V3V2) and kQ(V2V1V2V1)
or
kQ(RV3V2) and kQ(RV2V1)
Clearly V2V1>V3V2
Thus
kQ(RV3V2)>kQ(RV2V1)
Therefore spacing between surfaces decreases as potential increases i.e. r decreases.

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