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Two observers moving with different velocities see that a point charge produces same magnetic field at a point $A$. Their relative velocity must be parallel to , $ \overrightarrow r$ where $ \overrightarrow r$ is the position vector of point $A$ w.r.t. the point charge. This statement is

$\begin {array} {1 1} (a)\;True \\ (b)\;False \\ (c)\;Nothing\: can\: be\: said \\ (d)\;True\: only\: if\: the\: charge\: is\: moving\: perpendicular \: to \: \overrightarrow r \end {array}$


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Magnetic field is same, $ \therefore \overrightarrow V \times \overrightarrow r $ must be same.
$ ( \overrightarrow Vc- \overrightarrow Va) \times \overrightarrow r (\overrightarrow Vc - \overrightarrow Vb) \times \overrightarrow r$
$ \Rightarrow (\overrightarrow Vb - \overrightarrow Va) \times \overrightarrow r=0$
$( \overrightarrow Vc-\overrightarrow Va) || \overrightarrow r$
Ans : (a)
answered Feb 21, 2014 by thanvigandhi_1

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