Find the force between a uniformly charged
rod of length and having a charge Q and a
point charge a placed at a distance d from the
centre of the rod at its axial position.
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Explanation:
As a point charge q is situated at a distance r on axis from one end of a thin conducting of length L having charge Q as shown in figure.
Total charge=Q
Consider an elementary charge dq having length dx at a distance x from the charge q, then
dp=ρdx=
L
Q
dx
Now, force between dq and q
dF=
4πϵ
0
1
x
2
qdq
=K
Lx
2
qQdx
∴ Total force, F=∫dF=
L
KQq
∫
r
r+L
x
−2
dx
=
L
KQq
[−
x
1
]
r
r+L
=
L
−KQq
[
r+L
1
−
r
1
]
=
L
−KQq
[
(r+L)r
r−r−L
]=
r(r+L)
KQq
.
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