કોઈ એક ક્ષેત્રમાં સ્થિત વિદ્યુતક્ષેત્ર અને ચુંબકીયક્ષેત્ર પ્રવર્તે છે.ચુંબકીયક્ષેત્ર \(\vec B = {B_0}\left( {\hat i + 2\hat j - 4\hat k} \right)\) મુજબ આપવામાં આવે છે. જો એક વિજભાર આ ક્ષેત્રમાં \(\vec v = {v_0}\left( {3\hat i - \hat j + 2\hat k} \right)\) ના વેગથી ગતિ કરતો હોય ત્યારે કોઈ બળ અનુભવતો ના હોય તો \(SI\) એકમમાં વિદ્યુતક્ષેત્ર કેટલું હશે?

A \(\vec E = - {v_0}{B_0}\left( {3\hat i - 2\hat j - 4\hat k} \right)\)
B \(\vec E = - {v_0}{B_0}\left( {\hat i + \hat j + 7\hat k} \right)\)
C \(\vec E = {v_0}{B_0}\left( {14\hat j + 7\hat k} \right)\)
D \(\vec E = - {v_0}{B_0}\left( {14\hat j + 7\hat k} \right)\)

Verified Solution

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…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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