Question

find the electrical field at a distance s above one end of a line charge of length l​

Answer 1

Explanation:

Consider a small element dx of the line charge at a distance x from the point charge q.

Electric field at q due to small element dx,dE=

4πε

0

x

2

λdx

where λ=

l

Q

Force on q due to small element dF=qdE=q

l4πε

0

x

2

Qdx

∴F=

4πε

0

l

qQ

∫

r

r+l

x

2

dx

=

4πε

0

l

qQ

[

r

1

−

r+l

1

]

=

4πε

0

r(r+l)

qQ

Answer 2

$e = \frac{2pks}{( {s}^{2}) - \frac{ {l}^{2} }{4} {)}^{2} } | general \: eqn.$

$e = \frac{2pk}{ {s}^{3} } | for \: short \: dipole \\ that \: is.... \\ s > > > \frac{l}{2}$