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Question

A unit positive charge has to be brought from infinity to a mid-point between two charges, 20 μC and 10 μC separated by a distance of 50 m. How much work will be required by an external force?

A
2.1×104 J
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B
1.1×104 J
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C
3.1×104 J
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D
0.1×104 J
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Solution

The correct option is B 1.1×104 J
Given:
Point charge, qo=1 C

Let point M be the mid-point between the two charges.


At point M, total potential, VM=Vq1+Vq2
VM=kq1r1+kq2r2
VM=9×109×20×10625+9×109×10×10625
VM=1.1×104 V

We know, VM=Wext(M)qo
So, 1.1×104=Wext(M)1
Wext(M)=1.1×104 J

External force will have to do 1.1×104 J of work.

Why this question?Since potential at mid-point is greater than potential at infinity (v=0),the movementof charge is against its natural tendency.This gives hint that work has to be done by external force.

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