On the lower left corner of a square is a fixed charge qLL = 1.5x10^-9 C and on the loser right corner is a fixed charge qLR = 4.0x10^-9 C. The square has a side length L = 0.25 meters.
a) Find the electric potential energy of a third charge q = -6x10^-9 C placed at the upper left corner of this square.
b) Find the potential energy of this same third charge q placed at the upper right corner of the square.
Easy. Potential is a scalar, so add the voltage from each of the other charges.
Upper left Potential
V=kqLL/sidelength + kQLR/diagonal length
Then the electric potentialenergy of the third charge is
V*q
Do the same technique for the last charge, add the voltage potential from the three charges, then for elec potential energy, that sum times qur.
To find the electric potential energy for a given charge, we need to use Coulomb's Law and the formula for electric potential energy.
Coulomb's Law states that the force between two charges is given by:
F = k * (q1 * q2) / r^2
where F is the force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
The formula for electric potential energy is:
PE = k * (q1 * q2) / r
where PE is the electric potential energy.
a) To find the electric potential energy for the third charge q placed at the upper left corner of the square, we first need to find the force between q and qLL. The distance between them is equal to the length of the side of the square, L.
F = k * (q * qLL) / L^2
Substituting the given values:
F = (9 x 10^9 Nm^2/C^2) * (-6 x 10^-9 C * 1.5 x 10^-9 C) / (0.25 m)^2
Simplifying:
F = -216 N
Now, we can find the electric potential energy using the formula:
PE = k * (q * qLL) / L
Substituting the values:
PE = (9 x 10^9 Nm^2/C^2) * (-6 x 10^-9 C * 1.5 x 10^-9 C) / 0.25 m
Simplifying:
PE = -216 J
So the electric potential energy of the third charge q placed at the upper left corner of the square is -216 J.
b) To find the potential energy for the same charge q placed at the upper right corner of the square, we repeat the same steps as above, but this time using the value of qLR for the force calculation.
F = (9 x 10^9 Nm^2/C^2) * (-6 x 10^-9 C * 4.0 x 10^-9 C) / (0.25 m)^2
Simplifying:
F = -1152 N
PE = (9 x 10^9 Nm^2/C^2) * (-6 x 10^-9 C * 4.0 x 10^-9 C) / 0.25 m
Simplifying:
PE = -1152 J
So the potential energy of the third charge q placed at the upper right corner of the square is -1152 J.