A unit positive charge has to be brought from infinity to a mid-point between two charges, 20μC and 10μC separated by a distance of 50m. How much work will be required by an external force?
A
0.1×104J
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B
1.1×104J
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C
2.1×104J
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D
3.1×104J
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Solution
The correct option is B1.1×104J Given:
Point charge, qo=1C
Let point M be the mid-point between the two charges.
At point M, total potential, VM=Vq1+Vq2 ⇒VM=kq1r1+kq2r2 ⇒VM=9×109×20×10−625+9×109×10×10−625 ⇒VM=1.1×104V
We know, VM=Wext(∞→M)qo
So, 1.1×104=Wext(∞→M)1 ⇒Wext(∞→M)=1.1×104J
External force will have to do 1.1×104J 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.