Consider the electric force between a pair of charged particles a certain distance apart. By Coulomb's Law, if the charge on one

Question

4 years ago

8

of the particles is tripled, the force is _____.
one-half as much
one-third as much
two times as much
three times as much

1 answer:

Cloud [144] · Answer 1 · 2022-01-24T04:50:41+03:00

The electric force is three times as much

Explanation:

The magnitude of the electric force between two charged object is given by Coulomb's law:

$F=k\frac{q_1 q_2}{r^2}$

where:

$k=8.99\cdot 10^9 Nm^{-2}C^{-2}$ is the Coulomb's constant

$q_1, q_2$ are the two charges

r is the separation between the two charges

In this problem, let's call F the initial force between the two charges:

$F=k\frac{q_1 q_2}{r^2}$

Later, the charge on one of the particles is tripled, so that

$q_1' = 3 q_1$

Therefore, we can calculate the new electric force between the particles:

$F'=k\frac{q_1' q_2}{r^2}=k\frac{(3q_1)q_2}{r^2}=3(k\frac{q_1 q_2}{r^2})=3F$

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