A source consists of three charged particles located at the vertices of a square (see figure below), where the square has sides of length 0.213 m. The charges are q1 = 33.0 nC, q2 = −64.0 nC, and q3 = 54.5 nC. Find the electric potential at point A located at the fourth vertex.
www.webassign.net/katzpse1/26-p-032.png
potential is a acalar, not a vector. So find the potential from each corner (two of them are the same distance), and add.
V=v1+V2+V3=
To find the electric potential at point A, we can use the formula for electric potential due to multiple charges.
The electric potential at a point due to a single charge is given by the equation:
V1 = k * q1 / r1
Where:
V1 = Electric potential due to charge q1
k = Coulomb's constant (k = 9.0 x 10^9 N*m^2/C^2)
q1 = Charge at vertex 1 (33.0 nC)
r1 = Distance from point A to vertex 1
Similarly, for the other two charges, we have:
V2 = k * q2 / r2
V3 = k * q3 / r3
We can calculate the distances r1, r2, and r3 using the properties of a square. Since the sides of the square have a length of 0.213 m, r1 = r2 = r3 = 0.213 m.
Now, we can substitute the values into the equations to find the electric potential at point A.
V1 = (9.0 x 10^9 N*m^2/C^2) * (33.0 x 10^-9 C) / 0.213 m
V2 = (9.0 x 10^9 N*m^2/C^2) * (-64.0 x 10^-9 C) / 0.213 m
V3 = (9.0 x 10^9 N*m^2/C^2) * (54.5 x 10^-9 C) / 0.213 m
Now, we can add up the electric potentials due to each charge to find the total electric potential at point A:
V total = V1 + V2 + V3
Calculating these values will give us the electric potential at point A.