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:

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it