Forces Between Charges

The magnitude of the force exerted on a charge, q₁, due to another charge, q₂, a distance r away, is given by Coulomb's Law:

Coulomb's Law: F = kq₁q₂/r² where k = 8.99 x 10⁹ Nm²/C²

Since force is a vector, it has both a magnitude and a direction. The direction of the force is determined by the signs of the charges. If both charges have the same sign, they will repel and the direction of the force on q₁ will point directly away from q₂ along the line that joins them. If they have opposite signs, they will attract and the force on q₁ will point directly toward q₂.

Note that the force vectors on the two charges are equal and opposite. This is Newton's 3^rd law in action. This symmetry is apparent in the form of Coulomb's Law.

Notice how the magnitude of the force depends on the distance between the charges. Predict what will happen to the force if the distance is reduced by a factor of two, and use the simulation to verify your prediction.

Two unknown charges - Click on the milestone icon to answer a conceptual question that will appear in the milestone window at the upper right. Click the Explanation button to see a detailed solution to the milestone question.

In Milestone 1, if the charges are 4 cm apart and one is twice the magnitude of the other, what is the charge of the smaller one? Assume the force that you measure (by clicking on the charge) is in Newtons (N).

What happens if you have more than two charges? You may want to know the net force on a charge, q₁, due to a set of charges, q₂, q₃, q₄.... Since force is a vector, the net force on q₁ due to the set q₂, q₃, q₄,...is the vector sum of the forces due to each of the individual charges. That is:

F_1net = F₁₂ + F₁₃ + F₁₄ +...

Charges in an equilateral triangle - Click on the milestone icon to answer a conceptual question that will appear in the milestone window at the upper right. Remember that you can measure the force on a charge by clicking on that charge. Click the Explanation button to see a detailed solution to the milestone question.

In Milestone 2, if the equilateral triangle is 2 cm on a side, then what is the magnitude of the largest charge? Again, assume the force you measure is in Newtons (N).

Answers to questions:

• 0.32 C
• 0.37 C