How much work is done by an applied force that moves two charges of +7.8 µC that are initially very far apart to a distance of 3.8 cm apart
To determine the work done by an applied force, we need to know the electric field created by the charges. Assuming the charges are stationary, the charges create an electric field, and the force exerted by the applied force is opposite in direction to this electric field.
The formula to calculate the work done by a force is given by:
Work = Force * Distance * cos(theta)
Here, in our case, theta represents the angle between the force and displacement vectors, which will be 180 degrees since the force and displacement are in opposite directions (due to the opposite charges).
First, we need to calculate the force between the charges using Coulomb's law:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the charges,
k is the Coulomb's constant, approximately 9 × 10^9 N·m^2/C^2,
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
Plugging in the values:
F = (9 × 10^9 N·m^2/C^2) * |(7.8 µC * 7.8 µC)| / (0.038 m)^2
Note that we use the absolute value to represent the magnitude of the charge.
Then we can calculate the work using the equation mentioned earlier:
Work = Force * Distance * cos(180)
Now let's calculate the force first:
F = (9 × 10^9 N·m^2/C^2) * (7.8 × 10^-6 C * 7.8 × 10^-6 C) / (0.038 m)^2
After calculating, we find that the force between the charges is approximately 4.058 N.
Plugging this value into the work equation:
Work = (4.058 N) * (0.038 m) * cos(180)
Since cos(180) equals -1, the equation simplifies to:
Work = (4.058 N) * (0.038 m) * (-1)
Finally, calculating the work:
Work = -0.006163 N·m (or J)
So, the work done by the applied force to move the charges to a distance of 3.8 cm apart is approximately -0.006163 N·m (or J). The negative sign indicates that work is done against the force, as the applied force is moving in the opposite direction of the electric field.