The drawing shows a square, each side of which has a length of L = 0.250 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 = -6.00 x 10-9 C placed at corner A and then at corner B.
I do not know what your drawing looks like but
The major thing about potentials is that you can add them as independent scalars. They are not vectors with components.
if R1 is distance from your point to q1 and R2 is distance from your point to q2
you can find k q1 q3 / R1 and k q2 q3/R2 and just add them
see http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potpoi.html
By the way when the charges are the same sign the potential is + and if opposite it is -
so here both are - and the things will fly in from infinity if you let them go.
To find the electric potential energy of a third charge at different corners of the square, we need to use the formula for electric potential energy:
𝑉 = 𝑘 𝑞1 𝑞2 / 𝑟
where V is the electric potential energy, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges at the corners of the square, and r is the distance between the charges.
First, let's calculate the electric potential energy at corner A. We assume that q1 and q2 are positive charges since they are described as "two different positive charges."
1. Calculate the distance between the charges:
The distance between the charges is the length of the sides of the square. Given that each side has a length of L = 0.250 m, it means r = L.
2. Calculate the electric potential energy at corner A:
Using the formula mentioned earlier:
V_A = (k * q1 * q3) / r
Since the charge q3 is negative, it means it has a negative sign in q3.
Substituting the values into the formula:
V_A = (9 x 10^9 Nm^2/C^2 * q1 * q3) / L
3. Calculate the electric potential energy at corner B:
To find the electric potential energy at corner B, we need to calculate the new distance between the charges. Since q1 and q2 are positioned at the corners of the square, moving the charge q3 from corner A to corner B means the distance between the charges changes.
The new distance between the charges is the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:
d^2 = L^2 + L^2
d^2 = 2L^2
d = √(2L^2)
Now, we can substitute the new distance (d) into the formula and calculate the electric potential energy at corner B, similar to how we calculated V_A.
V_B = (k * q1 * q3) / d
Substituting the values into the formula:
V_B = (9 x 10^9 Nm^2/C^2 * q1 * q3) / √(2L^2)
By following these steps and substituting the given values, you can calculate the electric potential energy at corner A and B.