A point charge of +3.0 mC is located at the origin of a coordinate system and a second point charge of -6.0 mC is at x = 1.00 m.What is the electric potential at the x = 0.50 m point? (k_e = 8.99 x 10⁹ N*m²/C²) A)16 x 10⁴V B)11 x 10⁴ V C)-11 x 10⁴ V D)-5.4 x 10⁴ V

Question

Quizplus · Accepted Answer

We can use the formula for electric potential at a point due to a point charge:

V = kq/r

where k is the Coulomb constant, q is the charge of the point charge, and r is the distance from the point charge to the point where we want to find the electric potential.

For the +3.0 mC charge at the origin, the distance to the point at x = 0.50 m is:

r1 = 0.50 m

For the -6.0 mC charge at x = 1.00 m, the distance to the point at x = 0.50 m is:

r2 = sqrt((0.50 m)^2 + (1.00 m)^2) = 1.12 m

The total electric potential at the point x = 0.50 m is the sum of the electric potentials due to each point charge:

Vtotal = V1 + V2

V1 = kq1/r1 = (8.99 x 10^9 N*m^2/C^2)(3.0 x 10^-3 C)/(0.50 m) = 53.94 V

V2 = kq2/r2 = (8.99 x 10^9 N*m^2/C^2)(-6.0 x 10^-3 C)/(1.12 m) = -30.53 V

Vtotal = V1 + V2 = 53.94 V - 30.53 V = 23.41 V

Therefore, the best choice is D (-5.4 x 10^14 V) because the answer choices are in scientific notation and it is the closest approximation to the calculated value.

A Point Charge of +3