Electricity Coulomb’s Law Chapter 5

Coulomb’s Law Magic? (a)The two glass rods were each rubbed with a silk cloth and one was suspended by thread. When they are close to each other, they repel each other. (b)The plastic rod was rubbed with fur. When brought close to the glass rod, the rods attract each other.

Coulomb’s Law Electric Charge (a)Two charged rods of the same sign repel each other. (b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge.

Coulomb’s Law Materials classified based on their ability to move charge Conductors are materials in which a significant number of electrons are free to move. Examples include metals. The charged particles in nonconductors (insulators) are not free to move. Examples include rubber, plastic, glass. Semiconductors are materials that are intermediate between conductors and insulators; examples include silicon and germanium in computer chips. Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance.

Coulomb’s Law

The electrostatic force on particle 1 can be described in terms of a unit vector r along an axis through the two particles, radially away from particle 2. Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. If the particles have charges q 1 and q 2, are separated by distance r, and are at rest (or moving only slowly) relative to each other, then the magnitude of the force acting on each due to the other is given by

Coulomb’s Law The electrostatic force vector acting on a charged particle due to a second charged particle is either directly toward the second particle (opposite signs of charge) or directly away from it (same sign of charge). If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Coulomb’s Law Two charged particles repel each other if they have the same sign of charge, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge.

Coulomb’s Law Multiple Forces: If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces. Shell Theories: There are two shell theories for electrostatic force Answer: (a) left towards the electron (b) left away from the other proton (c) left

Coulomb’s Law

Example 4: The following three charges are arranged as shown. Determine the net force acting on the charge on the far right (q3 = charge 3). Solution :

Charge is Quantized Electric charge is quantized (restricted to certain values). The charge of a particle can be written as ne, where n is a positive or negative integer and e is the elementary charge. Any positive or negative charge q that can be detected can be written as in which e, the elementary charge, has the approximate value The charges and masses of the electron, proton and neutron are given in Table: charge and mass of the Electron, Proton and Neutron ParticleCharge (C)Mass (kg)

Charge is Quantized When a physical quantity such as charge can have only discrete values rather than any value, we say that the quantity is quantized. It is possible, for example, to find a particle that has no charge at all or a charge of +10e or -6e, but not a particle with a charge of, say, 3.57e. Answer: -15e

The Electric Field How does particle 1 “know” of the presence of particle 2? That is, since the particles do not touch, how can particle 2 push on particle 1—how can there be such an action at a distance? ?

The Electric Field The electric field E at any point is defined in terms of the electrostatic force F that would be exerted on a positive test charge q 0 placed there: Electric Field

The Electric Field Electric Field Lines Electric field lines help us visualize the direction and magnitude of electric fields. The electric field vector at any point is tangent to the field line through that point. The density of field lines in that region is proportional to the magnitude of the electric field there. (a) The force on a positive test charge near a very large, non-conducting sheet with uniform positive charge on one side. (b) The electric field vector E at the test charge’s location, and the nearby electric field lines, extending away from the sheet. (c) Side view.

The Electric Field Electric Field Lines Field lines for two particles with equal positive charge. Doesn’t the pattern itself suggest that the particles repel each other? (1)The electric field vector at any given point must be tangent to the field line at that point and in the same direction, as shown for one vector. (2) A closer spacing means a larger field magnitude.

The Electric Field

The capacitance

Electric Current As Fig. (a) reminds us, any isolated conducting loop—regardless of whether it has an excess charge — is all at the same potential. No electric field can exist within it or along its surface. If we insert a battery in the loop, as in Fig. (b), the conducting loop is no longer at a single potential. Electric fields act inside the material making up the loop, exerting forces on internal charges, causing them to move and thus establishing a current. (The diagram assumes the motion of positive charges moving clockwise.) Figure c shows a section of a conductor, part of a conducting loop in which current has been established. If charge dq passes through a hypothetical plane (such as aa’) in time dt, then the current i through that plane is defined as (c)

Electric Current Figure (a) shows a conductor with current i 0 splitting at a junction into two branches. Because charge is conserved, the magnitudes of the currents in the branches must add to yield the magnitude of the current in the original conductor, so that Figure (b) suggests, bending or reorienting the wires in space does not change the validity of the above equation Current arrows show only a direction (or sense) of flow along a conductor, not a direction in space. Answer: 8A with arrow pointing right

Electric Current

Resistance and Resistivity If we apply the same potential difference between the ends of geometrically similar rods of copper and of glass, very different currents result. The characteristic of the conductor that enters here is its electrical resistance. The resistance R of a conductor is defined as where V is the potential difference across the conductor and i is the current through the conductor. Instead of the resistance R of an object, we may deal with the resistivity ρ of the material: The reciprocal of resistivity is conductivity σ of the material: Assortment of Resistors

Power, Semiconductors, Superconductors

Resistance and Resistivity The resistance R of a conducting wire of length L and uniform cross section is Here A is the cross-sectional area. A potential difference V is applied between the ends of a wire of length L and cross section A, establishing a current i. The resistivity ρ for most materials changes with temperature. For many materials, including metals, the relation between ρ and temperature T is approximated by the equation Here T 0 is a reference temperature, ρ 0 is the resistivity at T 0, and α is the temperature coefficient of resistivity for the material. The resistivity of copper as a function of temperature.

Power, Semiconductors, Superconductors Figure shows a circuit consisting of a battery B that is connected by wires, which we assume have negligible resistance, to an unspecified conducting device. The device might be a resistor, a storage battery (a rechargeable battery), a motor, or some other electrical device. The battery maintains a potential difference of magnitude V across its own terminals and thus (because of the wires) across the terminals of the unspecified device, with a greater potential at terminal a of the device than at terminal b. The power P, or rate of energy transfer, in an electrical device across which a potential difference V is maintained is If the device is a resistor, the power can also be written as or,

Power