An electron with kinetic energy \(5 \mathrm{eV}\) enters a region of uniform magnetic field of \(3 \mu \mathrm{T}\) perpendicular to its direction. An electric field \(\mathrm{E}\) is applied perpendicular to the direction of velocity and magnetic field. electron moves along the same path, The value of \(\mathrm{E}\) is _______ \(\mathrm{NC}^{-1}\). (Given, mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\), electric charge \(=1.6 \times 10^{-19} \mathrm{C}\) )

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Answer & Solution

Correct Answer

(B) \(4\)

Detailed explanation

For the given condition of moving undeflected, net force should be zero.

\(\mathrm{qE} =\mathrm{qVB}\)

\(\mathrm{E} =\mathrm{VB}\)

\(=\sqrt{\frac{2 \times \mathrm{KE}}{\mathrm{m}}} \times \mathrm{B}\)

\(=\sqrt{\frac{2 \times 5 \times 1.6 \times 10^{-19}}{9 \times 10^{-31}}} \times 3 \times 10^{-6}\)

\(=4 \mathrm{~N} / \mathrm{C}\)

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