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.