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A particle is moving with velocity $ \hat i+ 3\hat j$ and it produces an electric field $ 2\hat k$ at a point. It will produce magnetic field at that point equal to

$\begin {array} {1 1} (a)\;6\hat i - 2\hat j / c^2 & \quad (b)\;6\hat i + 2\hat j / c^2 \\ (c)\;Zero & \quad (d)\;Cannot\: be\: determined\: from\: the\: given\: data \end {array}$

 

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A)
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This question is about manipulating the expressions for the electric and magnetic fields.
Also, to obtain the magnetic field, one needs to use the formula for moving charges.
$ \overrightarrow B = \large\frac{\mu_0}{4 \pi}$ $q \large\frac{\overrightarrow V \times \overrightarrow r}{r^3}$         .....(1)
$ \overrightarrow E = \large\frac{q}{4 \pi \in}$ $ \large\frac{ \overrightarrow r}{r^3}$             .......(2)
$ \mu_0 \in_0 = \large\frac{1}{c^2}$           ......(3)
substituting from (2) and(3) in (1)  we get  
 
Ans : (a)

 

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