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 : 1Step 1: Divide QQ 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(Q−q1)r2 ....(2)Step 3: Condition for force to be maximum The repulsive force between the charges will be maximum if, dFdq1=0 ⇒kr2(Q−2q1)=0 ⇒q1=Q2 Equation (1)⇒ q2=Q−Q2=Q2 Step 4: Ratio of Q:q1:q2 Q:q1:q2=Q:Q2:Q2=1:12:12 ⇒Q:q1:q2=2:1:1Hence, Option (D) is correct.

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