QJEEM20Phcb83: JEE Main 2020 Physics - Class 12 JEEM20Phcb83 Solution: A particle of mass m and charge q has an initial velocity v → = …

Question

Verified Solution • 2025–26 Session moderate

A particle of mass m and charge q has an initial velocity

\vec{v} = v_{0} \hat{j}

. If an electric field

\vec{E} = E_{0} \hat{i}

and magnetic field

\vec{B} = B_{0} \hat{i}

act on the particle, its speed will double after a time:

Accepted Answer

Electric field will increase the speed of particle in x direction.

F_x = qE

∴

a =

\frac{q E}{m}

Also v_x = at =

\frac{q E}{m}

t

v_{x}^{2} + v_{y}^{2} = v^{2}

\Rightarrow

v_{x}^{2} + v_{0}^{2} = {(2 v_{0})}^{2}

\Rightarrow

v_x =

\sqrt{3}

v₀

∴

\frac{q E}{m}

t =

\sqrt{3}

v₀

\Rightarrow

t =

\frac{\sqrt{3} m v_{0}}{q E_{0}}

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