Suppose a charge of -4x10
-6 C is at the origin and a charge of 2.5x10
-6 C is at the point
(0, 4) m. (a) Find the electric potential at P (3, 0) m, assuming the electric potential is zero at
infinity,
To find the electric potential at point P (3, 0) m, we can use the formula for electric potential due to point charges. The formula is:
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 magnitude of the charge, and r is the distance between the charge and the point at which we are calculating the potential.
First, let's calculate the potential due to the charge at the origin:
Q1 = -4 x 10^-6 C
r1 = distance between the origin (0, 0) and point P (3, 0) = 3 m
Using the formula, we have:
V1 = k * Q1 / r1
Substituting the given values, we get:
V1 = (9 x 10^9 Nm^2/C^2) * (-4 x 10^-6 C) / 3 m
Calculating this expression, we find:
V1 = -12 x 10^3 V
Next, let's calculate the potential due to the charge at point (0, 4) m:
Q2 = 2.5 x 10^-6 C
r2 = distance between point (0, 4) m and point P (3, 0) m
To find r2, we can use the distance formula:
r2 = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((3 - 0)^2 + (0 - 4)^2)
= sqrt(9 + 16)
= sqrt(25)
= 5 m
Using the formula again, we have:
V2 = k * Q2 / r2
= (9 x 10^9 Nm^2/C^2) * (2.5 x 10^-6 C) / 5 m
Calculating this expression, we get:
V2 = 4.5 x 10^3 V
Finally, to find the total electric potential at point P, we need to add the potentials due to the two charges:
V_total = V1 + V2
= (-12 x 10^3 V) + (4.5 x 10^3 V)
Calculating this expression, we find:
V_total = -7.5 x 10^3 V
Therefore, the electric potential at point P (3, 0) m, assuming the electric potential is zero at infinity, is -7.5 x 10^3 V.