Electric Charge and Electric Field

Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them.

Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them. Figure 21-14. Coulomb’s law, Eq. 21–1, gives the force between two point charges, Q1 and Q2, a distance r apart. Coulomb’s law, Eq. 21–1, gives the force between two point charges, Q1 and Q2, a distance r apart.

Properties of electric force between two stationary charge particles: The electric force.. is inversely proportional to square of the separation between particles and directed along the line joining them is proportional to the product of the charges q1 and q2 on the two particles is attractive if charges are of opposite sign and repulsive if the charges are of the same sign Is a conservative force

Coulomb’s Law equation An equation giving the magnitude of electric force between two point charges (Point charges defined as a particle of zero size that carries an electric charge) Where ke is called the Coulomb constant and ke = 8.9875 x 109 Nm2C-2 (S.I units) or ke = 1/ 4πЄ0 and Є0 = permittivity of free space = 8.8542 x 10-12 C2N-1m-2

Coulomb’s Law Coulomb’s law: This equation gives the magnitude of the force between two charges.

Coulomb’s Law The force is along the line connecting the charges, and is attractive if the charges are opposite, and repulsive if they are the same. The direction of the static electric force one point charge exerts on another is always along the line joining the two charges, and depends on whether the charges have the same sign as in (a) and (b), or opposite signs (c).

Coulomb’s Law Unit of charge: coulomb, C The proportionality constant in Coulomb’s law is then: Charges produced by rubbing are typically around a microcoulomb:

Coulomb’s Law Electric charge is quantized in units of the electron charge.

Coulomb’s Law The proportionality constant k can also be written in terms of , the permittivity of free space: (16-2)

Electric Force is a vector Figure 23.7 Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. The force F21 exerted by q2 on q1 is equal in magnitude and opposite in direction to the force F12 exerted by q1 on q2. (a) When the charges are of the same sign, the force is repulsive. Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. The force F21 exerted by q2 on q1 is equal in magnitude and opposite in direction to the force F12 exerted by q1 on q2. When the charges are of the same sign, the force is repulsive.

When the charges are of opposite signs, the force is attractive. Figure 23.7 Two point charges separated by a distance r exert a force on each other that is given by Coulomb’s law. The force F21 exerted by q2 on q1 is equal in magnitude and opposite in direction to the force F12 exerted by q1 on q2. (b) When the charges are of opposite signs, the force is attractive. When the charges are of opposite signs, the force is attractive.

Where, is a unit vector directed from q1 to q2. Since the force obeys Newton’s third law, then F12 = - F21

Example: Question 1 The electron and proton of a hydrogen atom are separated by a distance of approximately 5.3 x 10-11 m. Find the magnitude of the electric force.

Example: Solution 1 Fe = 8.2 x 10-8 N

Coulomb’s Law Example 2: Three charges in a line. Three charged particles are arranged in a line, as shown. Calculate the net electrostatic force on particle 3 (the -4.0 μC on the right) due to the other two charges. Solution: Coulomb’s law gives the magnitude of the forces on particle 3 from particle 1 and from particle 2. The directions of the forces can be found from the geometrical arrangement of the charges (NOT by putting signs on the charges in Coulomb’s law, which is what the students will want to do). F = -1.5 N (to the left).

Exercise What is the magnitude of the force a +25 µC charge exerts on a +2.5 mC charge 28 cm away?

Exercise 2. Three point charges, Q1 = 3 µC, Q2 = -5 µC, and Q3 = 8 µC are placed on the x-axis as shown in Figure 1. Find the net force on the charge Q2 due to the charges Q1 and Q3. Q1 20 cm 30 cm Q2 Q3

Exercise 3. Particles of charge +75, +48 and -85 µC are placed in a line . The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two.

Coulomb’s Law Example 3: Electric force using vector components. Calculate the net electrostatic force on charge Q3 shown in the figure due to the charges Q1 and Q2. Figure 21-18. Determining the forces for Example 21–3. (a) The directions of the individual forces are as shown because F32 is repulsive (the force on Q3 is in the direction away from Q2 because Q3 and Q2 are both positive) whereas F31 is attractive (Q3 and Q1 have opposite signs), so F31 points toward Q1. (b) Adding F32 to F31 to obtain the net force. Solution: The forces, components, and signs are as shown in the figure. Result: The magnitude of the force is 290 N, at an angle of 65° to the x axis.

Coulomb’s Law Approach We use Coulomb’s law to find the magnitude of the individual forces. The direction of each force will be along the line connecting Q3 to Q1 or Q2. The forces F31 and F32 have the directions shown in figure, Q1 exerts an attractive force on Q3 Q2 exerts a repulsive force on Q3 4. The forces F31 and F32 are not in the same line, so to find the resultant force on Q3, we resolve F31 and F32 into x and y components and perform vector addition.

Exercise Three charged particles are placed at the corners of an equilateral triangle of side 1.20 m . The charges are +7.0µC, -8.0µC and -6.0µC. Calculate the magnitude and direction of the net force on Q1 due to the other two.

Electrical Force with Other Forces, Example The spheres are in equilibrium. Since they are separated, they exert a repulsive force on each other. Charges are like charges Model each sphere as a particle in equilibrium. Proceed as usual with equilibrium problems, noting one force is an electrical force. Section 23.3

Electrical Force with Other Forces, Example cont. The force diagram includes the components of the tension, the electrical force, and the weight. Solve for |q| If the charge of the spheres is not given, you cannot determine the sign of q, only that they both have same sign. Section 23.3

Examples Two indentical small spheres, each having a mass of 3.00 x 10-2 kg, hang in equilibrium as shown in Figure. The length, L of each string is 0.150m and the θ= 5.000. Find the magnitude of the charge on each sphere.

Summary Two kinds of electric charge – positive and negative. Charge is conserved. Charge on electron: e = 1.602 x 10-19 C. Conductors: electrons free to move. Insulators: nonconductors.

Summary Charge is quantized in units of e. Objects can be charged by conduction or induction. Coulomb’s law: