Coulomb’s Law Section 20.3 1

Electric Force Electric force is a fundamental force that results from the interaction of one object that has an electric charge with another object that has an electric charge. Electric forces dominate the properties of objects in our everyday experiences. However, the large numbers of particle interactions that occur make it more convenient to treat everyday forces in terms of nonfundamental forces called contact forces, such as normal force, friction, and tension.

Fundamental Forces Gravitational forces and electric forces are the two fundamental forces we've studied so far. Gravitational forces are exerted at all size scales but dominate at the largest distance and mass scales (like planetary motion). Electromagnetic forces are also exerted at all scales but can dominate at the human scale (like friction, normal force, tension, etc.). Unlike gravity, which is always attractive, electric forces may be attractive or repulsive, depending upon the charges on the objects involved.

Review: Newton's Law of Universal Gravitation Mass is a property of matter. Two masses are gravitationally attracted to each other by the relationship:

Coulomb’s Law Charge is a property of matter. Two charged bodies are electrically attracted to each other or repelled by each other by the relationship:

Coulomb’s Law On your chart the equation looks like this: Coulomb’s law tells us how the magnitude of the force between two particles varies with their charge and with the distance between them. Leave the signs out of the calculations! Once you calculate the strength of the force, you will use the diagram to determine the direction.

                                                                                                             Coulomb's Law The electrostatic force is directed along the line joining the charges, and it is attractive if the charges have unlike signs and repulsive if the charges have like signs.

What’s Wrong Task A student’s diagram for the electric forces acting on two negatively charged (–Q and –4Q) particles is shown. Particle A has four times the mass of particle B. What, if anything, is wrong with this diagram? If something is wrong, explain the error and how to correct it. If the diagram is valid, explain why.

What’s Wrong Task: Solution According to Newton’s Third Law, if one object exerts a force on a second object, the second object always exerts a force of equal magnitude on the first object in the opposite direction. To correct the diagram the arrow on the +4Q charge could be shortened so that it is the same length as the one on the +Q charge.* *Not pictured is the very small attractive gravitational force between them.

Sample Problem A point charge of positive +12.0 μC experiences an attractive force of 51 mN when it is placed 15 cm from another point charge. What is the other charge?

Sample Problem: Solution 12

Ranking Task The following diagrams show three separate pairs of point charges. Rank the force on each point charge from most attractive to most repulsive. Explain your reasoning.

Ranking Task: Solution C = D > A = B > E = F The magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the separation distance. In terms of magnitude of force: C and D are first equal and greatest, E and F will be next, and A and B have the least magnitude. However, since E and F repel each other, they are placed last in this ranking.

Ranking Task In each case shown, a particle of charge +q is placed a distance d from a particle of charge +4q. The particles are then released simultaneously. The masses of the particles are indicated in the diagram. Rank the magnitude of the acceleration of each particle just after it is released. Explain your reasoning.

Ranking Task: Solution A = B = C > D Since all the forces acting on the particles are the same (based on Coulomb’s Law), the acceleration is determined by the force divided by the mass. All the particles either have a mass of m or 3m. All the particles with mass m will have the same larger acceleration and the particle with mass 3m has the smaller acceleration.

Superposition Electrical force, like all forces, is a vector quantity. If an object of interest interacts with several other objects, the net force is the vector sum of the individual forces.

Ranking Task In each figure, two charges are fixed in place on a grid, and a point near those particles is labeled P. All of the charges are the same size, Q, but they can be either positive or negative. Rank the strength (magnitude) of the electric force on a charge +q that is placed at point P. Explain your reasoning.

Ranking Task: Solution C > D > B > A In case C the two charges produce electric forces on q that both point to the left and have equal magnitude. In case D the two charges produce electric forces on q that both point to the right, but one is one-quarter of the other. In case B the two charges produce oppositely directed electric forces on q, but one is one-quarter of the other so they end up vector summing to a smaller net force. In case A the two charges produce oppositely directed electric forces on q that are equal in magnitude, so the net force is zero. Note that even though an object is at rest, there may be forces exerted on that object by other objects.

Ranking Task In each figure, three charges are fixed in place on a grid, and a point near those particles is labeled P. All of the charges are the same size, Q, but they can be either positive or negative. Rank the magnitude of the net electric force on a charge +q that is placed at point P. Explain your reasoning.

Ranking Task: Solution C > A > D > B Suppose we call the force between two charges Q separated by one block on the grid F. In case A, the forces all point to the right and have magnitude of F, 1/4F, and 1/9F, for a net force of 1.36F. In case B, the forces are F to the right, F to the left, and 1/4F to the right, for a net force of 0.25F to the right. In case C the forces are F to the left, F to the left, and 1/4F to the right, for a net force of 1.75F to the left. In case D, the forces are F to the right, 1/4F to the left, and 1/9F to the right, for a net force of 0.86F to the right.

Sample Problem Three charges are in a line along the x-axis. A -3 μC charge is at x = 1 m, a +2 μC charge is at x = 3 m, and a +4 μC charge is at x = 7 m. What is the force on the +4 μC charge?

Sample Problem: Solution 23

Sample Problem Three charges form a right triangle. There is a -3 μC charge. A +2 μC charge is 2 cm below the -3 μC charge. A +4 μC charge is 6 cm to the right of the +2 μC charge. What is the force on the +4 μC charge?

Sample Problem: Solution A separate video will be posted to the Learning Hub walking you through the solution to this problem. 25