Charges of +2.38 nC and -1.06 nC are located at opposite corners, A and C, respectively, of a square which is L = 1.13 m on a side. What is the electric potential at a third corner, B, of the square (where there is no charge)?
To find the electric potential at point B, we can use the principle of superposition, which states that the total electric potential at a point due to multiple charges is the sum of the electric potentials due to each individual charge.
The electric potential at a point due to a single point charge is given by the equation:
V = k * q / r
Where V is the electric potential, k is the electrostatic constant (9 * 10^9 Nm²/C²), q is the charge, and r is the distance from the charge to the point where you want to find the potential.
In this scenario, we have two charges: +2.38 nC at point A and -1.06 nC at point C. Point B is the third corner of the square, where there is no charge.
First, we need to calculate the distances from the charges to point B. Since the square has equal sides, the distance from A to B and from C to B will be equal and can be found using the Pythagorean theorem:
Distance AB = Distance CB = L * sqrt(2)
Substituting the given values, we have:
Distance AB = Distance CB = 1.13 m * sqrt(2)
Next, we calculate the electric potential due to each charge separately using the equation mentioned earlier:
Electric potential due to charge at A:
V_A = (9 * 10^9 Nm²/C²) * (2.38 * 10^(-9) C) / (1.13 m * sqrt(2))
Electric potential due to charge at C:
V_C = (9 * 10^9 Nm²/C²) * (-1.06 * 10^(-9) C) / (1.13 m * sqrt(2))
Finally, we find the total electric potential at point B by summing up the potentials due to each charge:
V_B = V_A + V_C
Calculating the values and adding them up will give you the electric potential at point B.