An electron is released from rest at the negative plate of a parallel plate capacitor and accelerates to the positive plate (see the drawing). The plates are separated by a distance of 1.3 cm, and the electric field within the capacitor has a magnitude of 2.7 x 106 V/m. What is the kinetic energy of the electron just as it reaches the positive plate?

0.007

9.4 X 10^-7

To calculate the kinetic energy of the electron just as it reaches the positive plate, we can use the formula for the electric potential energy of a charged particle in an electric field:

U = q * V

where U is the electric potential energy, q is the charge of the electron, and V is the electric potential difference.

Since the electron starts at rest, all of its initial potential energy is converted to kinetic energy when it reaches the positive plate. Therefore, the kinetic energy of the electron is equal to the electric potential energy U:

K.E. = U

The electric potential difference V can be calculated using the electric field strength E and the distance d between the plates:

V = E * d

Substituting this into the formula for U, we get:

K.E. = q * (E * d)

The charge of an electron is given by q = -e, where e is the elementary charge (1.6 x 10^-19 C). Therefore, the equation becomes:

K.E. = -e * (E * d)

Plugging in the values for e, E, and d, we get:

K.E. = - (1.6 x 10^-19 C) * (2.7 x 10^6 V/m) * (1.3 x 10^-2 m)

Calculating this expression will give us the kinetic energy of the electron just as it reaches the positive plate.

To find the kinetic energy of the electron just as it reaches the positive plate, we need to know the potential difference (voltage) across the capacitor. With that information, we can use the formula for kinetic energy (KE):

KE = (1/2)mv^2

Here's how you can calculate the potential difference (V) across the capacitor:

Step 1: Calculate the electric field strength (E) using the given magnitude. In this case, the electric field strength is 2.7 x 10^6 V/m.

Step 2: Calculate the potential difference (V) using the formula V = Ed, where E is the electric field strength and d is the separation distance of the plates.

V = (2.7 x 10^6 V/m) * (1.3 cm)

Note that we need to convert the separation distance from cm to meters because the electric field strength was given in V/m.

Step 3: Calculate the kinetic energy (KE) using the formula KE = (1/2)mv^2.

To determine the velocity (v) of the electron just as it reaches the positive plate, we can use the principle of conservation of energy. The potential energy (PE) at the negative plate is equal to the kinetic energy (KE) at the positive plate because there are no energy losses due to resistance or other factors. Mathematically, this can be written as:

PE = KE

Therefore, we have:

qV = (1/2)mv^2

where q is the charge of the electron and m is its mass. The charge of an electron is 1.6 x 10^-19 C, and its mass is 9.1 x 10^-31 kg. Rearranging the equation, we get:

v = sqrt((2*q*V) / m)

Now we can calculate v using the potential difference (V) and plug it into the kinetic energy formula to find the answer.