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Question

Two charges q1 and q2 are placed 30 cm apart as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in potential energy of the system is xq34πϵ0 where x is

A
6q2
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B
6q1
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C
8q2
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D
8q1
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Solution

The correct option is C 8q2

Given that,
AB=30 cm=0.3 m
AC=40 cm=0.4 m
Initially, q3 is at point C.
BC = AB2+AC2
BC = 0.32+0.42
BC=0.5 m

The initial potential energy of the system when charge q3 was at C,
Ui = k{q1q2AB+q1q3AC+q2q3BC}
Ui = 14πϵ0{q1q20.3+q1q30.4+q2q30.5}


Now, final potential energy of the system when charge q3 is moved from C to D,
Uf = 14πϵ0{q1q30.4+q1q20.3+q2q30.1}

So, Uf Ui = 14πε0{q2q30.1q2q30.5}

Uf Ui = 104πε0{q2q31q2q35}

Uf Ui = 104πϵo×4q2q35

Uf Ui =8q2q34πϵ0=xq34πϵ0 [given]

x=8q2

Hence, option (a) is correct.

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