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Question

A charge Q is divided into two parts q1 and q2 such that they experience maximum force of repulsion when separated by certain distance. The ratio of Q,q1 and q2 is :

A
1 : 1 : 2
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B
1 : 2 : 2
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C
2 : 2 : 1
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D
2 : 1 : 1
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Solution

The correct option is D 2 : 1 : 1
Step 1: Divide Q
Q is divided into two parts q1 andq2
Q=q1+q2 ....(1)

Step 2: Force of repulsion between q1 and q2
Let r be the distance between charges.
Using Coulomb's law, F=kq1q2r2=kq1(Qq1)r2 ....(2)

Step 3: Condition for force to be maximum
The repulsive force between the charges will be maximum if,
dFdq1=0
kr2(Q2q1)=0
q1=Q2

Equation (1) q2=QQ2=Q2

Step 4: Ratio of Q:q1:q2

Q:q1:q2=Q:Q2:Q2=1:12:12
Q:q1:q2=2:1:1

Hence, Option (D) is correct.

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