A charge of 4x10^(-3) coulombs exerts a force of 2,880 Nt on charge q2 at a distance of 0.461 m. The size of q2 is most nearly____
A- 0.017 mC
B- 0.032 mC
C- o.32 mC
D- 3.2 mC
E- 0.025 uC
F- 0.050 uC
g- 2.17 C
To determine the size of charge q2, we can use the formula for the electric force between two charges:
\[ F = \frac{{k \cdot q_1 \cdot q_2}}{{r^2}}\]
Where:
F = force between two charges (in Newtons)
k = Coulomb's constant (approximately 9.0 × 10^9 Nm^2/C^2)
q1 = charge 1 (in Coulombs)
q2 = charge 2 (unknown, to be determined)
r = distance between the charges (in meters)
We can rearrange the formula to solve for q2:
\[ q_2 = \frac{{F \cdot r^2}}{{k \cdot q_1}}\]
Now, let's substitute the given values into the formula:
F = 2,880 Nt
r = 0.461 m
k = 9.0 × 10^9 Nm^2/C^2
q1 = 4 × 10^(-3) C
\[ q_2 = \frac{{2,880 \ \text{Nt} \times (0.461 \ \text{m})^2}}{{9.0 \times 10^9 \ \text{Nm}^2/\text{C}^2 \times 4 × 10^(-3) \ \text{C}}}\]
Simplifying the equation:
\[ q_2 = \frac{{2,880 \times 0.461^2}}{{9.0 \times 10^9 \times 4 \times 10^(-3)}}\]
\[ q_2 = \frac{{3779.248}}{{3.6 \times 10^7}}\]
\[ q_2 \approx 0.1049 \times 10^(-2) \ \text{C} \]
To convert the result to microcoulombs (uC), we divide by 10^(-6):
\[ q_2 \approx 0.1049 \times 10^(-2) \ \text{C} = 0.1049 \ \text{uC} \]
The size of q2 is approximately 0.1049 uC.
None of the answer choices match this result exactly since they are expressed in different units. The closest option is E- 0.025 uC.