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Question

Two charges q1 and q2 are placed 30cm apart as shown. A third charge q3 is moved along the circle of radius 40cm from C to D. The change in the potential energy of the system is q3K4πϵ0

Find K?

596378_b2286aa882da42d79036ca77e7f5f921.png

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

The correct option is A 8q2
Given two charges q1 and q2 are placed 30cm apart as shown inn the figure. A third charge q3 moved from C to D.
Radius =40cm
Given the change in potential energy of the system is q3k4πε0. We have to find the value of k.
We solve it as follows:
The change in potential energy of system is UDUC as discussed under:
When charge q3 is at C, then its potential energy is UC=14πε0[q1q30.4+q2q30.5]
when charge q3 is at D, then UD is
UD=14πε0[q1q30.4+q2q30.1]
Hence, change in potential energy is ΔU
ΔU=14πε0[q2q30.1q2q30.5] ...(i)
But given, ΔU=q3k4πε0 ...(ii)
On equating (i) and (ii), we get
q3k4πε0=14πε0[q2q30.1q2q30.5]
We get,
k=q2(102)=8q2

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