Question

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 magnitude of force on the particle at that instant ? ($d$ is much larger than the dimensions of the dipole)

• A. $\sqrt{2}\left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{{\left(d/2\right)}^3}\times qv$
• B. $\left(\frac{{\mu }_0}{4\pi }\right)\frac{2M}{{\left(d/2\right)}^3}\times qv$
• C. $\left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{{\left(d/2\right)}^3}\times qv$
• D. $0$

Answer 1

Answer: (D)

$B_1=2\left(\frac{{\mu }_0}{4\pi }\right)\frac{M}{{\left(d2\right)}^3};B_2=\left(\frac{{\mu }_0}{4\pi }\right)\frac{2M}{{\left(d2\right)}^3}$
$B_1=B_2$
$\Rightarrow B_{net}$ is at $45^{\circ }\left(\theta =45^{\circ }\right)$
velocity of charge and $B_{net}$ are parallel so by $\vec{F}=q(\vec{v}\times \vec{B})$ force on charge particle is zero.