The drawing shows six point charges arranged in a rectangle. The value of q is 3.15 μC, and the distance d is 0.321 m. Find the total electric potential at location P, which is at the center of the rectangle.
To find the total electric potential at location P, we need to consider the contributions from each of the six point charges.
The formula to calculate the electric potential due to a point charge is given by:
V = k * q / r
Where:
- V is the electric potential
- k is the electrostatic constant, approximately equal to 9 x 10^9 N m^2/C^2
- q is the charge of the point charge
- r is the distance from the point charge to the location of interest
Since we have six point charges in this case, we need to calculate the electric potential due to each of them and then sum them up to get the total electric potential at location P.
Let's go step by step:
1. Calculate the electric potential due to each point charge. Using the given values, we have:
- q = 3.15 μC (microCoulombs)
- The distance between the charges and location P is half the width of the rectangle, which is d/2 = 0.321 m / 2 = 0.1605 m
Using the formula, we can calculate the electric potential due to each point charge:
V1 = k * q / r
V1 = (9 x 10^9 N m^2/C^2) * (3.15 x 10^-6 C) / 0.1605 m
Similarly, calculate V2, V3, V4, V5, and V6 using the same formula.
2. Add up all the calculated electric potentials to get the total electric potential at location P:
Total electric potential at location P = V1 + V2 + V3 + V4 + V5 + V6
By substituting the values into the equation and performing the calculations, you will obtain the total electric potential at location P.