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## Electric Charge and Electric Field

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**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. 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 109Nm2C-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**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.**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.**Exercise**• What is the magnitude of the force a +25 µC charge exerts on a +2.5 mC charge 28 cm away?**Q1**Q2 Q3 20 cm 30 cm 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.**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.**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: