Final answer:
The potential difference between two points from a point charge is calculated using the formula V = k * Q (1/r1 - 1/r2). For a 3.0 µC charge and points at 10 cm and 20 cm, the calculated potential difference is 44.95 V, which does not match any provided options, suggesting a potential issue with the question or answers.
Step-by-step explanation:
The potential difference between two points in an electric field created by a point charge is given by the formula V = k * Q (1/r1 - 1/r2), where V is the electric potential difference, k is Coulomb's constant (8.99 x 10^9 N*m^2/C^2), Q is the charge in coulombs, r1 and r2 are the distances from the charge to the two points, respectively. For a 3.0 µC charge and points at 10 cm and 20 cm, the potential difference is calculated as:
V = (8.99 x 10^9) * (3.0 x 10^-6) * (1/0.1 - 1/0.2) = 8.99 x 10^3 * (10 - 5) = 8.99 x 10^3 * 5 = 4.495 x 10^4 V
To find the potential difference in volts, we convert the result to units of volts by dividing by 1000 (because there are 1000 millivolts in a volt), which gives us 44.95 V. Since this value does not match any of the options provided, it appears there may be a calculation error or a misunderstanding in the question's values or units.
However, if the calculated potential difference was intended to be one of the options provided and not 44.95 V, there could be an error in the question or the answer choices. If this is a practice problem, we should ensure that both the question and the answer choices are formulated correctly.