JEE Mains · Physics · STD 12 - Moving charges and magnetism
- JEE Mains 2017
- Medium
- MCQ
In a certain region static electric and magnetic fields exist. The magnetic field is given by \(\vec B = {B_0}\left( {\hat i + 2\hat j - 4\hat k} \right)\). If a test charge moving with a velocity \(\vec v = {v_0}\left( {3\hat i - \hat j + 2\hat k} \right)\) experiences no force in that region, then the electric field in the region, in \(SI\, units\), is
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Answer & Solution
Correct Answer
(D) \(\vec E = - {v_0}{B_0}\left( {14\hat j + 7\hat k} \right)\)
Step-by-step Solution
Detailed explanation
According to question, as the test charge experiences no net force in that region i.e., sum of electric force \(\left( {{{\text{F}}_{\text{e}}} = {\text{q}}\overrightarrow {\text{E}} } \right)\,\) and magnetic forces \([{{\text{F}}_{\text{m}}} = {\text{q}}(\overline {\text{v}} \times \overline {\text{B}} ]\) will be zero.
Hence, \(F_{e}+F_{m}=0\)
\(\mathrm{F}_{\mathrm{e}}=-\mathrm{q}(\overline{\mathrm{v}} \times \overline{\mathrm{B}})\)
\(=-\mathrm{B}_{0} \mathrm{v}_{0}[(3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \times(\mathrm{i}+2 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})]\)
\(=-B_{0} v_{0}(14 \hat{j}+7 \hat{k})\)
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