Question

A particle (m = 20 mg, q = -5.0 μC) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 25 m/s in the positive x direction and is passing through the origin. How far is the particle from the origin at t = 2.0 s?

Answer 1

To find the displacement of the charged particle, calculate the force due to the electric field, then the resultant acceleration, and apply the kinematic equation for displacement.

Step-by-step explanation:

The question involves calculating the displacement of a particle with a known mass (20 mg) and charge (-5.0 μC) moving in a uniform electric field (60 N/C) after a given time (2.0 s). Since the particle has a charge and is exposed to an electric field, it will experience a force in the direction opposite to the electric field (because it has a negative charge). The force on the particle is given by F = qE, and the acceleration can be calculated using a = F/m. Once the acceleration is known, we can find the displacement using kinematic equations.

First, convert the mass to kilograms (m = 20 mg = 20 x 10-6 kg) and the charge to coulombs (q = -5.0 μC = -5.0 x 10-6 C). Calculate the force (F = qE) and the resultant acceleration (a = F/m). The displacement can then be found using the kinematic equation s = ut + 0.5at2, where 'u' is the initial velocity (25 m/s), 'a' is the acceleration, and 't' is the time (2.0 s).