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CBSE Class 12 Physics 2020 Delhi Set 3 Paper

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Question : 6
Total: 7
(a) Two point charges +Q1 and −Q2 are placed r distance apart. Obtain the expression for the amount of work done to place a third charge Q3 at the midpoint of the line joining the two charges.
(b) At what distance from charge +Q1 on the line joining the two charges (in terms of Q1,Q2 and r) will this work done be zero?
Solution:  
(a) Potential at the mid point of the line joining the charges Q1 and −Q2 is
V=k‌
Q1
r
2
+k‌
Q2
r
2
( r is the distance between Q1 and −Q2 )
Or, V=‌
2kQ1
r
−‌
2kQ2
r
Work done to place Q3 is W=V×Q3
Or, W=(‌
2kQ1
r
−‌
2kQ2
r
)×Q3
∴‌‌W=‌
2k
r
(Q1−Q2)Q3
(b) Work done will be zero when V=0
Let us consider that a point at a distance x from the charge Q1 where the potential will be zero.
So, ‌
kQ1
x
−‌
kQ2
r−x
=0
Or, ‌
Q1
x
−‌
Q2
r−x
=0
Or, ‌‌‌
Q1
x
=‌
Q2
r−x

Or, Q1(r−x)=Q2x
∴‌‌x=‌
Q1r
Q1+Q2

So, at a distance ‌
Q1r
Q1+Q2
 from charge Q1 on the line joining the two charges, the work done will be zero.
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