Question 90: Magnetism and Matter

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 = 45° 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)

Accepted Answer

$${\overrightarrow F _m} = q\left( {\overrightarrow V  	imes \overrightarrow B } ight)$$
$$\overrightarrow B  = {\overrightarrow B _x} + {\overrightarrow B _y}$$
Since M
y
= 2M
x
$$ \Rightarrow \left| {{{\overrightarrow B }_x}} ight| = \left| {{{\overrightarrow B }_y}} ight|$$
$${\overrightarrow B _{net}}$$ is parallel to $$\overrightarrow V $$
$$ \Rightarrow $$ $$\overrightarrow F  = 0$$

Answer

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

Answer

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

Answer

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

Answer

0

Magnetism and Matter

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