AP EAMCET · PHYSICS · Magnetic Effects of Current

Two short magnets of equal dipole moments \(M\) are fastened perpendicularly at their centres. The magnitude of the magnetic field at a distance \(d\) from the centre on the bisector of the right angle is ( \(\mu_0=\) Permeability of free space)

A \(\frac{\mu_0}{4 \pi} \frac{2 \sqrt{2} M}{d^3}\)
B \(\frac{\mu_0}{4 \pi} \frac{5 M}{d^3}\)
C \(\frac{\mu_0}{4 \pi} \frac{2 M}{d^3}\)
D \(\frac{\mu_0}{4 \pi} \frac{10 M}{d^3}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mu_0}{4 \pi} \frac{2 \sqrt{2} M}{d^3}\)

Step-by-step Solution

Detailed explanation

When two short magnets of equal dipole moments \(M\) are fastened perpendicularly at their centres. Then their resultant dipole moment is given as \(\begin{aligned} M^{\prime} & =\sqrt{M_1^2+M_2^2+2 M_1 M_2 \cos \theta} \\ & =\sqrt{M^2+M^2+2 M M \cos 90^{\circ}}\end{aligned}\)…

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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