Two adjacent corners of a square have charges q1 = +1.5 x 10-9 C and q2 = +4.0 x 10-9 C. The length of a side of the square L = 0.25 m. Find the EPE of a charge q3= -6.0 x 10-9 C placed at the 2 remaining corners.
I assume that EPE stands for Electrical Potential Energy. Are you asking for the total EPE of the complete configuration of 4 charges? It is confusing when you talk of the EPE of A (one) charge q3 placed at two corners.
The way you compute the EPE of one charge Q3, relative to a an energy of zero when the charge is at infinite dstance, is to add up the k Qi Q3/ri terms due to the other charges Qi at distance ri. k is Boltzmann's cosntant.
To find the Electric Potential Energy (EPE) of a charge q3 placed at the 2 remaining corners of the square, we can use the formula:
EPE = k * (q1 * q3 / r1,3 + q2 * q3 / r2,3)
where
- EPE is the Electric Potential Energy
- k is the electrostatic constant, approximately equal to 9 x 10^9 Nm^2/C^2
- q1, q2, q3 are the charges on the corners of the square
- r1,3, r2,3 are the distances between q1 and q3, and q2 and q3, respectively.
In this case, we have:
- q1 = +1.5 x 10^(-9) C
- q2 = +4.0 x 10^(-9) C
- q3 = -6.0 x 10^(-9) C
- L = 0.25 m (length of a side of the square)
We need to find the distances r1,3 and r2,3. Since the square is a regular square, the diagonal is equal to the side length multiplied by the square root of 2.
The distance r1,3 is the diagonal of the square, which is equal to:
r1,3 = L * √2
Substituting the values, we have:
r1,3 = 0.25 m * √2
Similarly, the distance r2,3 is also equal to:
r2,3 = L * √2
Substituting the values, we have:
r2,3 = 0.25 m * √2
Now, substituting all the values into the formula for EPE, we get:
EPE = (9 x 10^9 Nm^2/C^2) * [(1.5 x 10^(-9) C * -6.0 x 10^(-9) C) / (0.25 m * √2) + (4.0 x 10^(-9) C * -6.0 x 10^(-9) C) / (0.25 m * √2)]
Evaluating this expression will give us the Electric Potential Energy (EPE) of the system.