A proton is acted on by an uniform electric field of magnitude 233 N/C pointing in the positive x direction. The particle is initially at rest.
(a) In what direction will the charge move?
(b) Determine the work done by the electric field when the particle has moved through a distance of 3.15 cm from its initial position.
J
(c) Determine the change in electric potential energy of the charged particle.
J
(d) Determine the speed of the charged particle.
m/s
(a) To determine the direction in which the charge will move, we need to apply the right-hand rule for positive charges in an electric field. The right-hand rule states that if you point your thumb in the direction of the electric field, then the direction in which your fingers curl represents the direction of the positive charge's motion. In this case, since the electric field points in the positive x-direction, the charge will move in the same direction, which is the positive x-direction.
(b) The work done by the electric field can be calculated using the equation:
Work = Force * Distance * cos(theta)
where Force is the magnitude of the electric field, Distance is the distance over which the charge moves, and theta is the angle between the force and displacement vectors (which is 0 degrees in this case because the force and displacement vectors are parallel).
Given:
Force = 233 N/C
Distance = 3.15 cm = 0.0315 m
theta = 0 degrees
Substituting the given values into the formula, we get:
Work = 233 N/C * 0.0315 m * cos(0 degrees)
= 7.3395 J
Therefore, the work done by the electric field when the particle has moved through a distance of 3.15 cm is 7.3395 J.
(c) The change in electric potential energy of the charged particle can be calculated using the equation:
Change in potential energy (ΔPE) = -Work
In this case, the work done by the electric field is positive (as it is contributing energy to the particle) but the change in potential energy is the negative of the work done because work done by a conservative force, like the electric field, removes potential energy from the system.
ΔPE = -7.3395 J
Therefore, the change in electric potential energy of the charged particle is -7.3395 J.
(d) The speed of the charged particle can be determined using the principle of conservation of energy. The initial kinetic energy of the particle is zero since it is initially at rest, and the final kinetic energy is given by:
Final kinetic energy = Change in potential energy
Therefore:
1/2 * m * v^2 = -7.3395
Since the mass of the charged particle is not given, we cannot directly solve for the speed (v).