Question
A potential difference of 10.0 volts exists between two points, A and B, within an electric field. What is the magnitude of charge that requires 2.0 x 10-2 joule of work to move it from A to B? (1) 5.0 X 10^2 C (3) 5.0 x 10^-2 C (2) 2.0 x 10^-1 C (4) 2.0 x 10^-3 C
Answers
GPT-4o mini
To find the magnitude of charge \( q \) that requires \( 2.0 \times 10^{-2} \) joules of work \( W \) to move it through a potential difference \( V \) of \( 10.0 \) volts, we can use the formula:
\[
W = qV
\]
Rearranging the formula to solve for charge \( q \), we have:
\[
q = \frac{W}{V}
\]
Substituting the known values:
\[
q = \frac{2.0 \times 10^{-2} \text{ J}}{10.0 \text{ V}} = \frac{2.0 \times 10^{-2}}{10.0} = 2.0 \times 10^{-3} \text{ C}
\]
Thus, the magnitude of the charge required is:
\[
q = 2.0 \times 10^{-3} \text{ C}
\]
So the correct answer is (4) \( 2.0 \times 10^{-3} \text{ C} \).
\[
W = qV
\]
Rearranging the formula to solve for charge \( q \), we have:
\[
q = \frac{W}{V}
\]
Substituting the known values:
\[
q = \frac{2.0 \times 10^{-2} \text{ J}}{10.0 \text{ V}} = \frac{2.0 \times 10^{-2}}{10.0} = 2.0 \times 10^{-3} \text{ C}
\]
Thus, the magnitude of the charge required is:
\[
q = 2.0 \times 10^{-3} \text{ C}
\]
So the correct answer is (4) \( 2.0 \times 10^{-3} \text{ C} \).