The figure below shows four charges located at the corners of a square with sides of length a = 8.0 cm. If the charges
q1, q2, q3, and q4, are all 4.0 Coulomb, then:
To determine the electric potential energy of the system, we first need to calculate the potential energy between each pair of charges, and then sum them up.
The formula for electric potential energy between two point charges is:
U = (k * |q1 * q2|) / r
Where:
U is the electric potential energy
k is the Coulomb constant (k = 8.99 x 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
Let's calculate the potential energy between each pair of charges:
1. q1 and q2:
The distance between q1 and q2 is the length of the side of the square, a = 8.0 cm.
So, the potential energy between q1 and q2 is:
U12 = (k * |q1 * q2|) / a
2. q1 and q3:
The distance between q1 and q3 is the diagonal of the square.
The diagonal of the square can be calculated using the Pythagorean theorem:
d = sqrt((a^2) + (a^2)) = sqrt(2a^2) = sqrt(2) a
So, the potential energy between q1 and q3 is:
U13 = (k * |q1 * q3|) / d
3. q1 and q4:
The distance between q1 and q4 is also the diagonal of the square.
So, the potential energy between q1 and q4 is:
U14 = (k * |q1 * q4|) / d
Now, we can sum up the potential energies:
Total potential energy = U12 + U13 + U14
Substituting the values, we have:
Total potential energy = (k * |q1 * q2|) / a + (k * |q1 * q3|) / d + (k * |q1 * q4|) / d
Plugging in the values of k = 8.99 x 10^9 N m^2/C^2, q1 = q2 = q3 = q4 = 4.0 C, and a = 8.0 cm, we can calculate the total potential energy.