The nuclear charge (Ze) is non–uniformly distributed within a nucleus of radius R. The charge density ρ(r) [charge per unit volume] is dependent only on the radial distance r from the center of the nucleus as shown in figure. The electric field is only along the radial direction.
(i) The electric field at r = R is:
Text Solution
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(i) Electric field at r = R
E = 
where Q = Total charge within the nucleus = Ze
So E = 
So electric field is independent of
(ii)
Sol. Q = 
for a = 0, 
∴ 
or Q = 
(R – r) 4 πr 2 dr
= 
= 
= 
∴ Q = Ze = 
or d = 
(iii) From the formula of uniformly (volume) charged solid sphere
E = 
For E ∝ r, ρ should be constant throughout the volume of nucleus
This will be possible only when a = R.
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