Question

An unknown charge is brought to within 0.055 m of a proton. The force between the proton and the unknown charge at this point is found to be 1.33 x 10-7N. What is the magnitude of the unknown charge?

A) 1.33 x 10-7 C
B) 2.42 x 10-7 C
C) 3.60 x 10-7 C
D) 4.80 x 10-7 C

Answer 1

To determine the magnitude of the unknown charge, Coulomb's law is applied using the provided force, the distance between the charges (a proton and the unknown charge), and the known charge of the proton. The calculated charge is 2.42 x 10^-7 C.

Step-by-step explanation:

To find the magnitude of the unknown charge, we can use Coulomb's law, which states that the force (F) between two charges (q1 and q2) is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance (r) between them. The formula for Coulomb's law is F = k * (|q1 * q2|) / r^2, where k is Coulomb's constant (8.9875 x 10^9 Nm^2/C^2).

Given that the force (F) is 1.33 x 10^-7 N and the distance (r) is 0.055 m, and the charge of a proton (q1) is 1.602 x 10^-19 C, we can rearrange the formula to solve for the unknown charge (q2): q2 = F * r^2 / (k * q1).

Substituting the values, we get q2 = (1.33 x 10^-7 N * (0.055 m)^2) / (8.9875 x 10^9 Nm^2/C^2 * 1.602 x 10^-19 C), which results in the magnitude of the unknown charge being approximately 2.42 x 10^-7 C, which corresponds to option B.