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Q.

Within a spherical charge distribution of charge density  ρ(r), N equipotential surfaces of potential V0,V0+ΔV,V0+2ΔV,...V0+NΔV(ΔV>0), are drawn and have increasing radii r0,r1,r2,...rN, respectively. If the difference in the radii of the surfaces is constant for all values of  V0 and ΔV  then

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a

ρ(r)1r

b

ρ(r)r

c

ρ(r)1r2

d

ρ(r)=constant

answer is C.

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Detailed Solution

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WKT, E=dVdr

Here, ΔVandΔr are same for any pair of surfaces

So , E=Constant

Now electric field inside the spherical charge distribution 

E=ρ30r

E would be constant if  

ρ r=constant 

ρ(r)1r

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