Question

12. A solid sphere of radius R has a charge Q
distributed in its volume with a charge
densityp = kra, where kand a are constants and
ris the distance from its centre. If the electric
field at r = – is= times that at r = R. find the
R
value of
1) 2
2)3
3) 2.5
4) 0.2
​

Answer 1

Answer:

Explanation:

Using Gauss's law, we have

∮  

E

.d  

A

=  

ϵ  

0

​

 

1

​

∫(ρdv)=  

ϵ  

0

​

 

1

​

∫  

0

R

​

kr  

a

×4πr  

2

dr

or E×4πR  

2

=(  

ϵ  

0

​

 

4πk

​

)  

(a+3)

R  

(a+3)

 

​

 

For r=  

2

R

​

.E  

2

​

=  

ϵ  

0

​

(a+3)

k(  

2

R

​

)  

a+1

 

​

 

Given, E  

2

​

=  

8

E  

1

​

 

​

 

or  

ϵ  

0

​

(a+3)

k(  

2

R

​

)  

a+1

 

​

=  

8

1

​

 

ϵ  

0

​

(a+3)

kR  

(a+1)

 

​

 

∴2  

a+1

1

​

 

=  

8

1

​

 

or a=2.