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 θ = 45º 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)

Engineering

Physics

Magnet and Magnetic Dipole

Question

$\sqrt{2} (\frac{μ_{0}}{4 π}) \frac{M}{{(d / 2)}^{3}} \times qv$

$(\frac{μ_{0}}{4 π}) \frac{2 M}{{(d / 2)}^{3}} \times qv$

$(\frac{μ_{0}}{4 π}) \frac{M}{{(d / 2)}^{3}} \times qv$

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$B_{1} = 2 (\frac{μ_{0}}{4 π}) \frac{M}{{(d / 2)}^{3}}; B_{2} = (\frac{μ_{0}}{4 π}) \frac{2 M}{{(d / 2)}^{3}}$

B₁ = B₂

⇒ B_net is at 45° (θ = 45°)

Velocity of charge and B_net are parallel so

$\vec{F} = q (\vec{b} \times \vec{B})$ force on charge particle is zero.