Question:

Two parallel plates, 10 cm apart, create an electric field between them. The electric field is uniform and has a magnitude of 500 N/C directed from positive to negative plates. A positive point charge of 2 µC is released from rest at a distance of 5 cm from the positive plate.

a) What is the magnitude and direction of the electric force acting on the point charge? b) Calculate the acceleration of the point charge. c) How long does it take for the point charge to reach the negative plate?

Useful Constants: Charge of an electron = -1.6 x 10^-19 C Mass of an electron = 9.1 x 10^-31 kg

Note: Assume the point charge is a particle with negligible mass.

Answer:

a) The electric force exerted on a charged particle in an electric field can be calculated using the formula F = qE, where F is the force, q is the charge, and E is the electric field. The direction of the force is determined by the polarity of the charge.

Given: Charge of the point charge, q = 2 µC = 2 x 10^-6 C Electric field, E = 500 N/C

Substituting the values into the formula: F = (2 x 10^-6 C) x (500 N/C) F = 1 x 10^-3 N

The magnitude of the electric force acting on the point charge is 1 x 10^-3 N. Since the point charge is positive, the force is directed from the negative plate towards the positive plate.

b) Since the point charge has a negligible mass, we can use Newton's second law, F = ma, to determine its acceleration in the electric field.

Using the rearranged formula a = F/m: a = (1 x 10^-3 N) / (0 kg) a = ∞

The acceleration of the point charge is infinite. This implies that the point charge will experience a constant force and accelerate continually until it reaches the negative plate.

c) The time taken for the point charge to reach the negative plate can be calculated using the equation s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time taken.

Given: Distance traveled, s = 5 cm = 0.05 m (since 1 cm = 0.01 m) Initial velocity, u = 0 m/s Acceleration, a = ∞ (as calculated in part b)

Using the rearranged formula t = √(2s/a): t = √((2 x 0.05 m) / ∞) t = 0

Therefore, the time taken for the point charge to reach the negative plate is 0 seconds. This implies that the point charge reaches the negative plate instantaneously.