A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by Ex = -2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0, what is the speed of the particle at t = 2.0 s?

20 m/s

Explanation:

The force experienced by a charged particle in an electric field is given by

where, in this problem:

is the charge of the particle

E is the electric field

The electric field here has components:

So the components of the force experienced by the particle are:

Now we can find the components of the acceleration experienced by the particle, using Newton's second law of motion:

where

m = 4.0 g = 0.004 kg is the mass of the particle

The 3 components of the acceleration are:

Now we can find the components of the velocity of the particle at time t using the suvat equation:

where:

are the initial components of the velocity

Therefore, at t = 2.0 s, we have:

And so, the speed of the particle is the magnitude of the final velocity:

heat the gas and measure the pressure