Question

If the force exerted by an electric dipole on a charge \(q\) at a distance of 1 m is \(F\), the force at a point 2 m away in the same direction will be

• A. \(\frac{F}{2}\)
• B. \(\frac{F}{4}\)
• C. \(\frac{F}{6}\)
• D. \(\frac{F}{8}\)

Hint:

For a dipole, field and force vary as \(1/r^3\), so doubling distance reduces force by \(8\) times.

Answer 1

The Correct Option is D

Step 1: Recall electric field due to dipole on axial line.
Electric field due to dipole at distance \(r\) on axial line is:
\[ E \propto \frac{1}{r^3} \]
Step 2: Force on charge \(q\).
\[ F = qE \Rightarrow F \propto \frac{1}{r^3} \]
Step 3: Compare force at \(r=1m\) and \(r=2m\).
\[ \frac{F_2}{F_1} = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
Step 4: Write final relation.
\[ F_2 = \frac{F_1}{8} = \frac{F}{8} \]
Final Answer:
\[ \boxed{\frac{F}{8}} \]