A charged particle is released from rest in a region that has a uniform electric field of magnitude 64.0 N/C. After traveling a distance of 0.500 m in this region, the particle has a kinetic energy of 0.880 J. The charge on the particle is _______ C
force = E q
force * distance = work done = Ke = Eqd
so
.880 = 64.0 * q * 0.500
solve for q
To find the charge on the particle, we can use the following steps:
Step 1: Determine the work done by the electric field on the particle.
The work done by the electric field on a charged particle can be calculated using the formula:
Work = Electric Field Strength x Distance x Cosine(angle)
In this case, the work done is equal to the change in kinetic energy of the particle:
Work = 0.880 J
The distance traveled by the particle is 0.500 m, and the electric field strength is 64.0 N/C. Since the particle is released from rest, the angle between the electric field and the direction of motion is 0 degrees (cosine(0) = 1).
Substituting the given values into the formula, we have:
0.880 J = (64.0 N/C) x (0.500 m) x (cosine(0))
Step 2: Solve for the electric charge.
The electric field strength (E) can be related to the charge (q) and the force (F) acting on the particle using the formula:
F = q x E.
The force exerted on the particle is equal to the work done by the electric field, which we calculated to be 0.880 J.
Substituting the known values into the formula, we have:
0.880 J = q x (64.0 N/C)
Solving for q, we can divide both sides of the equation by 64.0 N/C:
q = 0.880 J / 64.0 N/C
Calculating the value of q using a calculator, we find:
q ≈ 0.01375 C
Therefore, the charge on the particle is approximately 0.01375 C.