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 q = 45Â° 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)

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 q = 45Â° 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)

$ \left( {{{{\mu _0}} \over {4\pi }}} \right){2M \over {{{\left( {d/2} \right)}^3}}} \times qv$

$ \left( {{{{\mu _0}} \over {4\pi }}} \right){M \over {{{\left( {d/2} \right)}^3}}} \times qv$

$\sqrt 2 \left( {{{{\mu _0}} \over {4\pi }}} \right){M \over {{{\left( {d/2} \right)}^3}}} \times qv$

Solution

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