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## Homework Statement

A particle of specific charge q/m is projected from the origin of coordinates with initial velocity ##v_1\hat{i}+v_2\hat{j}## in space having uniform electric field and magnetic field as ##-E\hat{j}## and ##-B\hat{j}## respectively. The particle will definitely return to the origin once if

A) ##\frac{v_1B}{\pi E}## is an integer

B) ##\frac{v_2B}{\pi E}## is an integer

C) ##\frac{\sqrt{{v_1}^2+{v_2}^2}B}{\pi E}## is an integer

D) ##\frac{q}{m}\frac{\sqrt{{v_1}^2+{v_2}^2}B}{\pi E}## is an integer

## Homework Equations

Lorentz force = ##q\vec{v}## x ##\vec{B} + q\vec{E}##

## The Attempt at a Solution

The force on the charged particle will be ##\vec{F} = qBv_y\hat{i} - qE\hat{j}- qBv_x\hat{k}## .

There will be a force on the particle in negative z- direction which means particle will never return to origin . I am not sure how to move forward .

Please help me .

Thanks

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