Question

An electron is moving with velocity `v_0 hat i`. If a uniform electric field `vec E = E_0 hat j` is set up in the region, the electron will ______.

Options

• describe a circular path.

• describe a helical path.

• describe a parabolic path.

• continue moving without any deviation.

Answer 1

An electron is moving with velocity `v_0 hat i`. If a uniform electric field `vec E = E_0 hat j` is set up in the region, the electron will describe a parabolic path.

Explanation:

The electron has an initial velocity along the x-direction (v_x = v₀). The electric field is applied along the y-direction (E_y = E₀).

The force acting on the electron is:

`vec F = -e vec E`

= `-e E_0 hat j`

This produces a constant acceleration in the y-direction:

a_y = `-(e E_0)/m`

Since x = v₀t and y = `1/2 a_y t^2`,

Eliminating the time:

y ∝ x²

It represents a parabolic trajectory.