First slide

Force on a charged particle moving in a magnetic field

Question

A particle is moving with velocity $\vec{v} = \hat{i} + 3 \hat{j}$ and it produces an electric field at a point given by $\vec{E} = 2 \hat{k}$ . It will produce magnetic field at that point equal to (all quantities are in SI units)

Moderate

A

$(6 \hat{i} - 2 \hat{j}) μ_{0} ε_{0}$
B

$(6 \hat{i} + 2 \hat{j}) μ_{0} ε_{0}$
C

zero
D

cannot be determined from the given data

Solution

$\begin{array}{l} \vec{E} = \frac{q}{4 π ε_{0} r^{2}} \hat{k} = 2 \hat{k} \\ \vec{B} = \frac{μ_{0}}{2 π} \frac{q \vec{v}}{r^{2}} \hat{r} = μ_{0} ε_{0} [\frac{q}{4 π ε_{0} r^{2}}] (\hat{i} + 3 \hat{j}) \times \hat{k} \end{array}$

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