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 (as shown in the figure below ). 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 principles of electrostatics and apply the concept of electric potential. The electric potential at a point is defined as the amount of work done to bring a unit positive charge from infinity to that point.
In this scenario, we have two charges located at opposite corners of a square: +2.38 nC at point A and -1.06 nC at point C. We need to find the electric potential at point B.
To calculate the electric potential at B, we need to consider the contribution of the electric potential due to each charge. The electric potential V at a point due to a point charge q can be calculated using the formula:
V = k * (q / r)
where k is the Coulomb's constant (k ≈ 8.99 × 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point where we want to find the electric potential.
First, let's calculate the electric potential due to the charge at point A. The distance between point A and B is the length of the side of the square, which is L = 1.13 m. The charge at A is +2.38 nC. Therefore, the electric potential at point B due to the charge at A can be calculated as:
V_A = k * (q_A / r_A)
where q_A = +2.38 nC and r_A = L.
Next, we need to calculate the electric potential due to the charge at point C. The distance between point C and B is also L = 1.13 m. The charge at C is -1.06 nC. Therefore, the electric potential at point B due to the charge at C can be calculated as:
V_C = k * (q_C / r_C)
where q_C = -1.06 nC and r_C = L.
The total electric potential at point B is given by the sum of the electric potentials due to the charges at A and C:
V_B = V_A + V_C
Finally, we can substitute the values of the charges and the length of the square side into the above equations to calculate the electric potential at point B.