In a certain region static electric and magnetic fields exist. The magnetic field is given by B → = B 0 i ^ + 2 j ^ - 4 k ^ . If a test charge moving with a velocity v → = v 0 3 i ^ - j ^ + 2 k ^ expe

Question

In a certain region static electric and magnetic fields exist. The magnetic field is given by B → = B 0 i ^ + 2 j ^ - 4 k ^ . If a test charge moving with a velocity v → = v 0 3 i ^ - j ^ + 2 k ^ experiences no force in that region, then the electric field in the region, in SI units, is:

TestHub · Accepted Answer

The total force experienced by test charge is $\vec{F_{e}} + {\vec{F}}_{m} = 0$ .

$F_{e} = - F_{m}$

$F_{e} = - q_{0} v_{0} B_{0} (\vec{V} \times \vec{B})$

$F_{e} = - q_{0} v_{0} B_{0} [(3 \hat{i} - \hat{j} + 2 \hat{k}) \times (\hat{i} + 2 \hat{j} - 4 \hat{k})]$

${\vec{F}}_{e} = - q v_{0} B_{0} (14 \hat{j} + 7 \hat{k})$

The electric field produced by the test charge is $∵ \vec{E} = \frac{{\vec{f}}_{e}}{q} = - v_{0} B_{0} (14 \hat{j} + 7 \hat{k})$

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