Find the magnitude of the acceleration (in m/s2) for an electron in a uniform electric field with a magnitude of 100 N/C.

Question

Find the magnitude of the acceleration (in m/s2) for an electron in a uniform electric field with a magnitude of 100 N/C.

and

Find the time it takes (in sec) for an electron initially at rest in a uniform electric field of 110 N/C to reach a speed of 0.01c (where c is the speed of light).

THANK YOU

Answer 1

To find the magnitude of the acceleration of an electron in a uniform electric field, we can use the equation a = F/m, where F is the force and m is the mass of the electron.

In this case, the magnitude of the electric field is given as 100 N/C. The force experienced by the electron in the electric field can be calculated using the equation F = q * E, where q is the charge of the electron. The charge of an electron is approximately -1.6 x 10^-19 C.

Substituting the values into the equation, we have F = (-1.6 x 10^-19 C) * (100 N/C) = -1.6 x 10^-17 N.

The mass of an electron is approximately 9.11 x 10^-31 kg.

Now, we can calculate the acceleration: a = (-1.6 x 10^-17 N) / (9.11 x 10^-31 kg) ≈ -1.76 x 10^13 m/s^2.

Note that the negative sign indicates that the direction of acceleration is opposite to the direction of the electric field.

For the second part of the question, to find the time it takes for an electron to reach a certain speed, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time.

The final velocity is given as 0.01c, where c is the speed of light. The speed of light is approximately 3 x 10^8 m/s.

Substituting the values into the equation, we have 0.01c = 0 + (-1.76 x 10^13 m/s^2) * t.

Simplifying the equation gives us t = (0.01c) / (-1.76 x 10^13 m/s^2).

Now, we can calculate the time: t = (0.01 * 3 x 10^8 m/s) / (-1.76 x 10^13 m/s^2) ≈ -170 s.

Note that the negative sign indicates that the time taken is in the opposite direction of the acceleration. In this case, it means it will take approximately 170 seconds for the electron to reach the given speed, but the direction will be opposite to the electric field.