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Need clarity, kindly explain! - Magnetic Effects of Current and Magnetism - JEE Main-4

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 $\theta=45^{\circ}$ with the horizontal line , as shown in figure. what would be the magnetitude of force on the particle at that instant? (d is much large than the dimensions of the dipole)

• Option 1)

$\left ( \frac{\mu_{0}}{4\pi} \right )\frac{M}{\left ( \frac{d}{2} \right )^{3}}\times qv$

• Option 2)

0

• Option 3)

$\sqrt{2}\left ( \frac{\mu_{0}}{4\pi} \right )\frac{M}{\left ( \frac{d}{2} \right )^{3}}\times qv$

• Option 4)

$\left ( \frac{\mu_{0}}{4\pi} \right )\frac{2M}{\left ( \frac{d}{2} \right )^{3}}\times qv$

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$B_{1}=2\left ( \frac{\mu_{0}}{4\pi} \right )\frac{M}{ \frac{d}{2} }$

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

$B_{1}=B_{2}$

Net magnetic field will be at $45^{\circ}$

The direction of Bnet & velocity of charge is same,

hence charge will experience no force.

Option 1)

$\left ( \frac{\mu_{0}}{4\pi} \right )\frac{M}{\left ( \frac{d}{2} \right )^{3}}\times qv$

Option 2)

0

Option 3)

$\sqrt{2}\left ( \frac{\mu_{0}}{4\pi} \right )\frac{M}{\left ( \frac{d}{2} \right )^{3}}\times qv$

Option 4)

$\left ( \frac{\mu_{0}}{4\pi} \right )\frac{2M}{\left ( \frac{d}{2} \right )^{3}}\times qv$

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