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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 θ=45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant?

2(μ₀/4π)M(d/2)³×qv

(μ₀/4π)2M(d/2)³×qv

0

(μ₀/4π)M(d/2)³×qv

Solution:

Correct option is D. 0
B₁ = 2(μ₀/4π)M(d/2)³; B₂ =(μ₀/4π)2M(d/2)³
B₁ = B₂ ⇒ Bnet is at 45° (θ=45°)
velocity of charge and Bnet are parallel so by F→ = q(v→ × B→) force on charge particle is zero.