Two point charges of values q and 2q are kept at a distance d apart from each other in air. A third charge Q is to be kept along the line in such a way that the net force acting on q and 2q is zero. Calculate the position of Q in terms of q and d?
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Answer:
should be negative and it should be placed somewhere between q and 2q. Let Q is placed at a distance x from q and (d−x) from 2q.
For net force on q to be zero,
x
2
kqQ
=
d
2
kq(2q)
...(1)
For net force on 2q to be zero,
(d−x)
2
k2qQ
=
d
2
kq(2q)
...(2)
From (1) and (2),
x
2
1
=
(d−x)
2
2
or 2x
2
=d
2
−2dx+x
2
or x
2
+2xd−d
2
=0
or x=
2
−2d±
4d
2
+4d
2
=−d+d
2
(as Q in between q and 2q so negative value of x is invalid)
or x=
(
2
+1)
d(
2
−1)(
2
+1)
=
(
2
+1)
d
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