Electric Field in a Capacitor: Calculating Charge on the Positive Plate

How can we determine the amount of charge on the positive plate of a capacitor?

The circular plates of a capacitor have a radius of 1.0 m and are separated by 0.78 cm. If a free electron is released near the negative plate and hits the positive plate 18 x 10⁻⁹ s later, how do we calculate the charge on the positive plate?

Solution:

The charge on the positive plate of the capacitor can be calculated by utilizing the properties of the electric field and the motion of the electron, along with given constants and equations.

To solve this problem, we first need to understand the motion of the electron in the electric field between the plates of the capacitor. The electron accelerates towards the positive plate due to the uniform electric field E between the plates.

Neglecting other forces, we can calculate the velocity v of the electron using the equation of motion: v = u + at. Here, u is the initial velocity (which is zero), a is the acceleration, and t is the time taken by the electron to move between the plates.

Since the electron is under the influence of an electric force, we can use the equation a = F/m, where m is the mass of the electron and F is the electric force on the electron. The force F is equal to the product of the charge of the electron (e) and the electric field E.

The electric field E between the plates of the capacitor is given by E = V/d, where V is the voltage and d is the separation between the plates. Knowing that the field E is proportional to the charge Q, we can use the equations and given values to calculate the charge on the positive plate.

Finally, the calculated charge should be positive, as it is related to the positive plate of the capacitor. To convert the charge from Coulombs to nanoCoulombs, simply multiply by 10⁹.

Explore more about the electric field in a capacitor here.