Question

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.​

Answer 1

Answer:This may help you

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

​

.