The drawing shows four point charges. The value of q is 2.4 µC, and the distance d is 0.86 m. Find the total potential at the location P. Assume that the potential of a point charge is zero at infinity.

This is a question of electric potential difference created by point charges.

To give a visual picture of the drawing in the question line #1 is drawn diagonally at about 45 degrees increasing in height from left to right. At each end of the line is a circle with "-q" in it. Line #2 is perpendicular to Line #1 and touches the halfway point of Line #1 at "P". The free end of Line #2 and the midway point both have a cirle with "q" in it. On line #1 "d" is the distance between "-q" and "P", "P" and the "-q" of the opposite end. On Line #2"d" is the distance between "q" on the unattached end and the "q" in the center, and from "q" in the center and "P".

To find the total potential at location P, we need to calculate the individual potentials at P due to each point charge and then sum them up.

The formula to calculate the electric potential due to a point charge is given by:

V = kq/r

Where:
V is the electric potential,
k is the Coulomb's constant (approximately 9 x 10^9 Nm²/C²),
q is the magnitude of the point charge, and
r is the distance from the point charge to the location where we want to find the potential.

In this case, we have four point charges, two positive and two negative. We will calculate the potentials due to each charge individually and consider their signs when summing them up.

Let's go step-by-step:

1. Calculation for the potential due to the positive charge at the unattached end of Line #2:
V1 = kq/r1
= (9 x 10^9 Nm²/C²)(2.4 µC) / d

2. Calculation for the potential due to the negative charge at the center of Line #2:
V2 = -kq/r2
= -(9 x 10^9 Nm²/C²)(2.4 µC) / d

3. Calculation for the potential due to the positive charge at one end of Line #1:
V3 = kq/r3
= (9 x 10^9 Nm²/C²)(2.4 µC) / √(d^2 + (d/2)^2)

4. Calculation for the potential due to the negative charge at the other end of Line #1:
V4 = -kq/r4
= -(9 x 10^9 Nm²/C²)(2.4 µC) / √(d^2 + (d/2)^2)

Now, sum up all the individual potentials to get the total potential at location P:

Total potential at P = V1 + V2 + V3 + V4

Remember to consider the signs of the potentials due to positive and negative charges correctly.