Question

what could you do to increase the electric force between two charged particles by a factor of 16?
a. increase one particles charge by a factor of 4.
b. reduce one particles charge by a factor of 16.
c. increase one particles charge by a factor of 16.
d. reduce one particles charge by a factor of 4.

Explanation:

Step1: Recall Coulomb's Law

Coulomb's Law is \( F = k\frac{q_1q_2}{r^2}\), where \(k\) is the Coulomb constant, \(q_1\) and \(q_2\) are the charges of the two particles, and \(r\) is the distance between them.

Step2: Analyze the effect of changing charge

If we assume the distance \(r\) remains constant, the force \(F\) is directly proportional to the product of the charges (\(q_1q_2\)). If we increase one particle's charge (say \(q_1\)) by a factor of \(16\) (i.e., \(q_1'=16q_1\)), then the new force \(F'=k\frac{(16q_1)q_2}{r^2}=16k\frac{q_1q_2}{r^2} = 16F\).

Answer:

C. Increase one particle's charge by a factor of 16.