question_answer

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 midpoint P, at angle \[\theta ={{45}^{o}}\]with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimensions of the dipole)             [JEE Main 8-4-2019 Afternoon]

A) \[\sqrt{2}\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{M}{{{(d/2)}^{3}}}\times q\text{v}\]       

B) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{2M}{{{(d/2)}^{3}}}\times q\text{v}\]

C) \[\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{M}{{{(d/2)}^{3}}}\times q\text{v}\]

D) 0

Correct Answer: D

Solution :

\[{{B}_{1}}=2\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{M}{{{(d/2)}^{3}}};\,\,\,\,\,\,\,{{B}_{2}}=\left( \frac{{{\mu }_{0}}}{4\pi } \right)\frac{2M}{{{(d/2)}^{3}}}\] \[{{B}_{1}}={{B}_{2}}\] \[\Rightarrow \]\[{{B}_{net}}\] is at \[{{45}^{o}}(\theta ={{45}^{o}})\] velocity of charge and \[{{B}_{net}}\]are parallel so by \[\vec{F}=q\left( \text{\vec{v}}\times \text{\vec{B}} \right)\]force on charge particle is zero.