A charged particle with charge q enters a region of constant uniform and mutually orthogonal fields →E and →B with a velocity →v perpendicular to both →E and →B and comes out without any change in magnitude and direction of →v. Then,

→v=→E×→B/B2

→v=→B×→E/E2

→v=→E×→E/B2

→v=→E×→E/E2

A

→v=→E×→E/E2

B

→v=→B×→E/E2

C

→v=→E×→B/B2

D

→v=→E×→E/B2

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Solution

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Since there is no change in magnitude and direction of particle velocity. So, Force due to magnetic field is equal to force due to electric field. ⇒q(→V×→B)=−q→E ⇒→V×→B=−→E ⇒→V=→E×→B/B2

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