Question

The center of an electric dipole is placed at the origin, with the axis of the dipole along the x-axis. The dipole moment of the system is \(\vec p\), the distance between the two charges is 2a and each charge has magnitude q. The electric potential due to the dipole at a point P, r distance away from the origin, having position vector r depends only on: (given r >> a)
1. q, a
2. r, a
3. r, p
4. r, q 

Answer 1

Correct Answer - Option 3 : r, p

CONCEPT:

• Electric potential is equal to the amount of work done per unit charge by an external force to move the charge q from infinity to a specific point in an electric field.

\(⇒ V=\frac{W}{q}\)

• Potential due to a single charged particle Q at a distance r from it is given by:

\(⇒ V=\frac{Q}{4\piϵ_{0}r}\)

Where, 

ϵ0 is the permittivity of free space and has a value of 8.85 × 10-12 F/m in SI units

EXPLANATION:

• Potential due to a dipole with dipole moment \(\vec p\) at a point P(r,θ) having position vector \(\vec r\) with respect to the dipole moment orientation is given by (if r >> a):

\(⇒ V=\frac{\vec p \cdot\vec r}{4\piϵ_{0}r^3}\)

• Therefore the potential can be calculated if p and r are known.

Therefore option 3 is correct.