two charged plates are 2mm apart. An electron escapes from the negatively charged plate and reaches the positively charged plate in 1.2*10^-8 seconds. Find the electric field between the plates?

To find the electric field between the plates, we can use the equation:

Electric field (E) = Voltage (V) / Distance (d)

First, let's calculate the voltage (V) between the plates. Since the electron moves from the negatively charged plate to the positively charged plate, it gains electric potential energy. The change in potential energy can be calculated using the formula:

Change in Potential Energy = Charge (q) x Voltage (V)

The charge of an electron is 1.6 x 10^-19 Coulombs.

The change in potential energy is equal to the kinetic energy gained by the electron, which can be calculated using the formula:

Change in Potential Energy = (1/2) x Mass (m) x (Velocity (v))^2

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

We know the time it takes for the electron to reach the positively charged plate is 1.2 x 10^-8 seconds, so we can calculate the velocity (v) using the formula:

Velocity (v) = Distance (d) / Time (t)

Substituting the given values:

Velocity (v) = 2 mm / 1.2 x 10^-8 s

Now we can substitute this velocity value into the formula for kinetic energy:

Change in Potential Energy = (1/2) x (9.11 x 10^-31 kg) x (Velocity (v))^2

We can equate the two expressions for change in potential energy and solve for voltage (V):

Charge (q) x Voltage (V) = (1/2) x (9.11 x 10^-31 kg) x (Velocity (v))^2

Voltage (V) = (1/2) x (9.11 x 10^-31 kg) x (Velocity (v))^2 / Charge (q)

Next, we substitute the values for the charge and velocity:

Voltage (V) = (1/2) x (9.11 x 10^-31 kg) x [(2 mm / 1.2 x 10^-8 s)]^2 / (1.6 x 10^-19 C)

Simplifying this expression, we get the value of voltage (V).

Finally, we can calculate the electric field (E) using the formula:

Electric field (E) = Voltage (V) / Distance (d)

Substituting the values for voltage and distance:

Electric field (E) = Voltage (V) / 2 mm

Now, you can plug in the calculated values to find the electric field between the plates.