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JEE Main2017PhysicsMagnetic Effects of CurrentActual

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:

Options

  1. AE → =   - v 0   B 0 i ^ + j ^ + 7 k ^
  2. BE → =   - υ 0   B 0 3 i ^ - 2 j ^ - 4 k ^
  3. CE → =   v 0   B 0 14 j ^ + 7 k ^
  4. DE → = - v 0   B 0 14 j ^ + 7 k ^

Correct answer

D. E → = - v 0   B 0 14 j ^ + 7 k ^

Step-by-step solution

The total force experienced by test charge is F e → +   F → m = 0 . F e = - F m F e = − q 0 v 0 B 0 V → × B → F e = - q 0   v 0 B 0 3 i ^ -   j ^ + 2 k ^ × i ^ + 2 j ^ - 4 k ^ F → e =   - q v 0 B 0   ( 14 j ^   + 7 k ^ ) The electric field produced by the test charge is ∵       E → =   f → e q =   - v 0 B 0   (   14 j ^ + 7 k ^ )

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