Question

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy gained by the particle after moving a distance of y will be ______.

Options

• qEy

• q²Ey

• qE²y

• qEy²

Answer 1

A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy gained by the particle after moving a distance of y will be qEy.

Explanation:

Force on a charged particle in a uniform electric field E is given by,

F = qE = ma

where a is the acceleration of the charged particle.

⇒ `a = (qE)/m`

From the third equation of motion,

v² = u² + 2as

= `0 + 2 xx (qE)/my = (2qEy)/m`

∴ Kinetic energy of particle, KE = `1/2m"v"^2`

= `1/2m((2qEy)/m)` = qEy