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Question

Two point charges q1=1 μC and q2=+1 μC are located on the x axis, at x=0 m and at x=1 m respectively. The work that must be done by an external force to bring a third point charge q3=+1 μC from infinity to x=2 m is

A
1.5×103 J
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B
4.5×103 J
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C
2.5×103 J
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D
3×103 J
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Solution

The correct option is B 4.5×103 J
The work that must be done on q3 by an external force is equal to the difference of potential energy U when the charge is at x=2 m and the potential energy when it is at infinity.

W=UfUi

W=14πϵ0[q3q2(r32)f+q3q1(r31)f+q2q1(r21)f]14πϵ0[q3q2(r32)i+q3q1(r31)i+q2q1(r21)i]

Here, (r21)i=(r21)f

Also, (r32)i=(r31)i=

W=14πϵ0[q3q2(r32)f+q3q1(r31)f]

Substituting the values, we have

W=(9.0×109)(1012)[(1)(1)(1.0)+(1)(1)(2.0)]

W=4.5×103 J

Hence, option (b) is the correct answer.

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