A particle with charge −5 µC is located on
the x-axis at the point 10 cm , and a second
particle with charge 6 µC is placed on the
x-axis at −8 cm . What is the magnitude of the total electrostatic force on a third particle with charge
2 µC placed on the x-axis at −2 cm ? The
Coulomb constant is 8.9875 × 109 N · m2
Answer in units of N.

36.25 N

Explanation:

The magnitude of the electrostatic force between two charges is given by Coulomb's law:

where:

is the Coulomb's constant

are the magnitude of the two charges

r is the separation between the two charges

Moreover:

- The force is repulsive if the two  charges have same sign

- The force is attractive if the two charges have opposite sign

In this problem, we have 3 charges:

is the charge located at

is the charge located at

is the charge located at

The force between charge 1 and charge 3 is:

And since the two charges have opposite sign, the force is attractive, so the force on charge 3 is to the right (towards charge 1).

The force between charge 2 and charge 3 is:

And since the two charges have same sign, the force is repulsive, so the force on charge 3 is to the right (away from charge 2).

So the two forces on charge 3 have same direction (to the right), so the net force is the sum of the two forces:

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