An electron and a proton are placed at rest in a uniform electric field modulus equal to 520N / C. Calculate the speed of each particle of 48 ns after the latter has been released

To calculate the speed of each particle 48 ns after being released in the electric field, we can use the equations of motion and the formula for the force experienced by a charged particle in an electric field.

Let's start with the equation of motion for an object in constant acceleration:

v = u + at

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time

In this case, the particles start from rest, so their initial velocities (u) are zero.

Now, let's determine the acceleration experienced by each particle due to the electric field.

The force (F) experienced by a charged particle in an electric field is given by:

F = qE

Where:
F = force
q = charge of the particle
E = electric field strength

For an electron, the charge (q) is -1.6 x 10^-19 C.
For a proton, the charge (q) is +1.6 x 10^-19 C.

Substituting these values into the equation, we have:

Force on an electron (Fe) = (-1.6 x 10^-19 C) (520 N/C) = -0.832 x 10^-16 N
Force on a proton (Fp) = (1.6 x 10^-19 C) (520 N/C) = 0.832 x 10^-16 N

The force is directed opposite to the direction of the electric field for the electron and in the same direction for the proton.

Now, we can use Newton's second law of motion to find the acceleration (a) of each particle:

a = F / m

Where:
a = acceleration
F = force
m = mass of the particle

The mass of an electron (me) is 9.11 x 10^-31 kg.
The mass of a proton (mp) is 1.67 x 10^-27 kg.

Substituting the values, we have:

Acceleration of an electron (ae) = (-0.832 x 10^-16 N) / (9.11 x 10^-31 kg) ≈ -9.12 x 10^14 m/s^2
Acceleration of a proton (ap) = (0.832 x 10^-16 N) / (1.67 x 10^-27 kg) ≈ 4.98 x 10^10 m/s^2

Now, we can use the equation of motion to calculate the final velocities of the particles after 48 ns:

v = u + at

For the electron:
u = 0 (initial velocity)
a = -9.12 x 10^14 m/s^2 (acceleration)
t = 48 ns = 48 x 10^-9 s (time)

v = 0 + (-9.12 x 10^14 m/s^2) (48 x 10^-9 s) ≈ -438.24 m/s

For the proton:
u = 0 (initial velocity)
a = 4.98 x 10^10 m/s^2 (acceleration)
t = 48 ns = 48 x 10^-9 s (time)

v = 0 + (4.98 x 10^10 m/s^2) (48 x 10^-9 s) ≈ 2.39 x 10^9 m/s

Therefore, the speed of the electron after 48 ns is approximately 438.24 m/s (directed opposite to the electric field), and the speed of the proton is approximately 2.39 x 10^9 m/s (in the same direction as the electric field).