Question

A certain charge Q is to be divided into two parts, 4 and Q-9. What is q in terms of Q, if the
two parts, placed at a given distance apart, are to have maximum Coulomb repulsion?​

Answer 1

Answer:Q=2q

Explanation:

The electrostatic force of repulsion between the charge q and (Q−q) at separation r is given by

F=  

4πε  

0

​

 

1

​

   

r  

2

 

q(Q−q)

​

 =  

4πε  

0

​

 

1

​

   

r  

2

 

qQ−q  

2

 

​

 

If F is maximum, then ∂F/∂q=0

i.e.,  

4πε  

0

​

 

1

​

⋅  

r  

2

 

(Q−2q)

​

=0

As  

4πε  

0

​

r  

2

 

1

​

 is constant, therefore

Q−2q=0 or Q=2q