Four identical 12µC charges are placed at the corners of a square of sides 44 cm, with one additional 12µC charge placed at the center. Find the electric potential at the midpoint of one of the sides.
Add up the kQ/r values contributed by each of the five charges (four at the corners and one in the middle of the square). The distances (r) of the different charges will vary. Three of them are located a distance of 0.22 m away.
You will have to do a bit of geometry for distances of the other two. Drawing a figure will help.
k is the Coulomb's Law constant. I am sure you have heard of it.
To find the electric potential at the midpoint of one of the sides, we need to calculate the contributions from each of the charges.
The electric potential due to a point charge can be calculated using the equation:
V = k * q / r
Where:
- V is the electric potential
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q is the charge of the point charge
- r is the distance from the point charge to the location where we want to calculate the electric potential
We can start by calculating the potential due to the charges at the corners of the square. The distance from each corner charge to the midpoint of the side is half the length of the side. In this case, it is 44/2 = 22 cm = 0.22 m.
Using the equation for electric potential, the potential due to each corner charge is:
V1 = (9 x 10^9 Nm^2/C^2) * (12 x 10^(-6) C) / (0.22 m)
= (9 x 10^9 Nm^2/C^2) * (12 x 10^(-6) C) / (0.22)
= 5.727 x 10^4 V
Since all four corner charges are the same, the total potential due to the corner charges is 4 times V1:
V_corner = 4 * V1
= 4 * 5.727 x 10^4 V
= 2.291 x 10^5 V
Next, we calculate the potential due to the charge at the center. The distance from the center charge to the midpoint of the side is half the length of the side, i.e., 0.22 m.
Using the equation for electric potential, the potential due to the center charge is:
V_center = (9 x 10^9 Nm^2/C^2) * (12 x 10^(-6) C) / (0.22 m)
= 5.727 x 10^4 V
Finally, to find the total electric potential at the midpoint of the side, we add up the potentials due to the corner charges and the center charge:
V_total = V_corner + V_center
= 2.291 x 10^5 V + (5.727 x 10^4 V)
= 2.864 x 10^5 V
Hence, the electric potential at the midpoint of one of the sides is approximately 286,400 Volts.