Two charges q1 and q2 are placed 30cm apart as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40cm from C to D. The change in potential energy of the system is xq34πϵ0 where x is
A
8q1
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B
8q2
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C
6q2
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D
6q1
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Solution
The correct option is B8q2
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}