MHT CET · Physics · Magnetic Effects of Current

Two electric dipoles of moment \(\mathrm{P}\) and \(27 \mathrm{P}\) are placed on a line with their centres \(24 \mathrm{~cm}\) apart. Their dipole moments are in opposite direction. At which point the electric field will be zero between the dipoles from the centre of dipole of moment P?

A \(6 \mathrm{~cm}\)
B \(8 \mathrm{~cm}\)
C \(10 \mathrm{~cm}\)
D \(12 \mathrm{~cm}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(6 \mathrm{~cm}\)

Step-by-step Solution

Detailed explanation

Dipole of moment \(\mathrm{p}\) is at a distance \(\mathrm{x}\) from \(\mathrm{N}\)

At N,
\(\mid \mathrm{E} . \mathrm{F}\). due to dipole \(1|=| \mathrm{E}\). F. due to dipole \(2 \mid\)
\(
\begin{aligned}
& \therefore \quad \frac{1}{4 \pi \varepsilon_0} \cdot \frac{2 \mathrm{p}}{\mathrm{x}^3}=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{2(27 \mathrm{p})}{(24-\mathrm{x})^3} \\
& \therefore \quad \frac{1}{\mathrm{x}^3}=\frac{27}{(24-\mathrm{x})^3} \Rightarrow \mathrm{x}=6 \mathrm{~cm} .
\end{aligned}
\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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