The drawing shows a square, each side of which has a length of L = 0.25 m. Two different positive charges q1 and q2 are fixed at the corners of the square. Find the electric potential energy of a third charge q3 = -5 x 10-9 C placed at corner A and then at corner B
To find the electric potential energy of the third charge, q3, placed at corner A and then at corner B, we need to consider the interaction between q3 and q1 as well as q3 and q2.
The electric potential energy, PE, between two charges can be calculated using the formula: PE = (k * |q1 * q2|) / r
Where:
- PE is the electric potential energy
- k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2)
- q1 and q2 are the charges involved in the interaction
- r is the distance between the charges
For the initial case, where q3 is at corner A:
1. Calculate the distance between q1 and q3: The charges are fixed at the corners of a square, so the distance between q1 and q3 is the length of the diagonal of the square. The length of the diagonal can be found using the Pythagorean theorem: diagonal = sqrt(2) * side length of the square. Thus, the distance between q1 and q3 is L * sqrt(2).
2. Plug the values into the formula: PE1 = (k * |q1 * q3|) / (L * sqrt(2))
For the second case, where q3 is at corner B:
1. Calculate the distance between q2 and q3: The charges are fixed at the corners of a square, so the distance between q2 and q3 is also the length of the diagonal of the square, which is L * sqrt(2).
2. Plug the values into the formula: PE2 = (k * |q2 * q3|) / (L * sqrt(2))
Now, let's substitute the given values and calculate the electric potential energy in each case using the formula.
For the initial case, where q3 is at corner A:
PE1 = (8.99 x 10^9 N m^2/C^2) * (|q1| * |-5 x 10^-9 C|) / (0.25 m * sqrt(2))
For the second case, where q3 is at corner B:
PE2 = (8.99 x 10^9 N m^2/C^2) * (|q2| * |-5 x 10^-9 C|) / (0.25 m * sqrt(2))
Plugging in the values of q1, q2, and L, you can calculate both PE1 and PE2.