Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing through their mid-point P, at angle θ = 45o with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (d is much larger than the dimensions of the dipole)

(A) \left( {\frac{{{\mu _0}}}{{4\pi }}} \right)\frac{M}{{{{\left( {d/2} \right)}^3}}} \times {q^\upsilon }

(C) \left( {\frac{{{\mu _0}}}{{4\pi }}} \right)\frac{2M}{{{{\left( {d/2} \right)}^3}}} \times {q^\upsilon }

(D) \sqrt 2 \left( {\frac{{{\mu _0}}}{{4\pi }}} \right)\frac{M}{{{{\left( {d/2} \right)}^3}}} \times {q^\upsilon }

JEE Mains · Physics · STD 12 - Magnetism and matter

Two magnetic dipoles \(X\) and \(Y\) are placed at a separation \(d\), with their axes perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X\). A particle of charge \(q\) is passing through their mid-point \(P\), at angle \(\theta = 45^o\) with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (\(d\) is much larger than the dimensions of the dipole)

Pick an option to check your answer.

Verified Solution

Correct Answer

(B) \(0\)

Detailed explanation

\(B_{1}=2\left(\frac{\mu_{0}}{4 \pi}\right) \frac{M}{(d / 2)^{3}} ; B_{2}=\left(\frac{\mu_{0}}{4 \pi}\right) \frac{2 M}{(d / 2)^{3}}\)

\(B_{1}=B_{2}\)

\(\Rightarrow \) \(B_{net}\) is at \(45^{\circ}\left(\theta=45^{\circ}\right)\)

Velocity of charge and \(B_{net}\) are parallel so by

\(\overrightarrow{\mathrm{F}}=q(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{B}})\) force on charge particle is Zero.

Same subject

From JEE Mains