Final answer:
The internal energy of a system consisting of two point charges can be calculated using the formula U = k * (q1 * q2) / r. By rearranging the formula and substituting the given values, we can solve for the charges. In this case, the charges are -17 μC and 17 μC.
Step-by-step explanation:
The internal energy of a system of two point charges can be calculated using the formula:
U = k * (q1 * q2) / r
where U is the electric potential energy, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, we have the values of U and r, and we want to find the charges. Rearranging the formula, we can solve for q1 * q2:
q1 * q2 = (U * r) / k
Substituting the given values into the equation:
q1 * q2 = (-180 x 10^-6 J * 1.7 x 10^-2 m) / (9 x 10^9 Nm^2/C^2)
q1 * q2 = -3.06 x 10^-15 C^2
Since the total charge in the system is 34 x 10^-9 C, we can solve for q1 and q2:
q1 + q2 = 34 x 10^-9 C
q1 - 3.06 x 10^-15 C = 34 x 10^-9 C
q1 = 34 x 10^-9 C + 3.06 x 10^-15 C
q1 = 34 x 10^-9 C
q2 = 34 x 10^-9 C - 34 x 10^-9 C
q2 = 0 C
Therefore, the answer is b. -17 μC, 17 μC.