Two identical point charges are fixed to diagonally opposite corners of a square that is 0.6 m on a side. Each charge is +2.5 µC. How much work is done by the electric force as one of the charges moves to an empty corner?
work=differenceinpotential*q
The potential starting is kQ/.6(sqrt2)
the potential ending is kQ/.6
work=kq/.6(.707-1)
To find the work done by the electric force as one of the charges moves to an empty corner, we need to calculate the electrostatic potential energy difference between the initial state and the final state.
The work done by the electric force is equal to the change in potential energy (ΔU), which can be calculated using the formula:
ΔU = Uf - Ui
where Uf is the final potential energy and Ui is the initial potential energy.
The potential energy of a point charge in an electric field is given by the formula:
U = (k * q1 * q2) / r
where U is the potential energy, k is the electrostatic constant (9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, we have two charges, both with a magnitude of +2.5 µC. The distance between the charges is the length of the diagonal of the square.
The length of the diagonal of a square can be found using the Pythagorean theorem:
d = √(a^2 + a^2)
where d is the length of the diagonal and a is the side length of the square.
In this case, a = 0.6 m, so:
d = √(0.6^2 + 0.6^2) = √(0.36 + 0.36) = √0.72 ≈ 0.8485 m
Now we can calculate the initial potential energy (Ui) and final potential energy (Uf) using the formula:
Ui = (k * q1 * q2) / r_initial
Uf = (k * q1 * q2) / r_final
Substituting the given values:
Ui = (9 × 10^9 N m^2/C^2) * (2.5 × 10^-6 C) * (2.5 × 10^-6 C) / (0.8485 m)
Uf = (9 × 10^9 N m^2/C^2) * (2.5 × 10^-6 C) * (2.5 × 10^-6 C) / (0.6 m)
Now we can calculate the work done (ΔU):
ΔU = Uf - Ui
Finally, we can substitute the calculated values to find the work done by the electric force.