The electric potential at a point P which is on the line segment joining the two charges of an electric dipole:

A. Maybe zero.

B. Maybe non-zero.

C. Must be zero.

D. Must be non-zero.

EXPLANATION:

• Assume:
  • +q is placed at (a,0)
  • -q is placed at (-a,0)
• Potential at D(x,0) due to charge q placed at point A(a,0) is

\(⇒ V_{DA}=\frac{q}{4\piϵ_{0}({a-x)}}\)

• Potential at D(d,0) due to charge -q placed at point B(-a,0) is:

\(⇒ V_{DB}=\frac{-q}{4\piϵ_{0}({a+x)}}\)

• Total potential at D due to both charges placed at points A and B is:

⇒  V = VDA + VDB = \(\frac{q}{4\piϵ_{0}({a-x)}}\) + \(\frac{-q}{4\piϵ_{0}({a+x)}}\) = \(\frac{qx}{2\pi\epsilon_{0}(a^{2}-x^{2})}\)

• If x is positive, the electric potential is positive.
• If x is negative, the electric potential is negative.
• If x is zero, the electric potential is zero.
• Therefore option 1 is correct.