Mention two differences between potential due to a point
charge and potential due to an electric dipole. Also derive an
expression for the electric potential at a point on the extended
axis of an electric dipole.
Answers
Answer:
Explanation:
Consider an electric dipole AB in which point charges +q and -q are separated by a distance 2l. Let P be a point on it's axis seperated by a distance r from the dipole's center O.
Electric dipole moment, p = q (2l)
Electric potential (V
A
) due to +q charge
V
A
=
4πϵ
0
1
r−l
q
Electric potential (V
B
) due to +q charge
V
B
=
4πϵ
0
1
r+l
−q
Therefore, total electric potential at P due to dipole will be
V=
4πϵ
0
q
[d
r−l
1
−
r+l
1
]
=
4πϵ
0
q
r
2
−l
2
2l
=
4πϵ
0
p
r
2
−l
2
1
Now, l<<r (short dipole)
V=
4πϵ
0
p
r
2
1
(for axial position)
For equatorial position, V=0 as charges are equal in magnitude with opposite signs they cancel each other's effect.
Answer:
Difference between potential due to a point