Chapter 21. Electric Charge and Electric Field

Transcription

1 1.1 Electric Charge Chapter 1 Electric Charge and Electric Field Only varieties of electric charges exist in nature; positive and negative charges. Like charges repel each other, while opposite charges attract each other. The unit of charge in the metric system is the Coulomb (C). Electric charge is quantized in units of the proton charge of e = 1.60x10-19 C. That is, electric charge q exists in discrete packets, and we can write q=ne, where N is some integer. Charge is conserved it can be transferred but not created nor destroyed. 1. Conductors and Insulators A. Conductors Materials in which electrons in the outer shell of the atoms are not bound to the nuclei of particular atoms, but are free to wander in the material. These so-called free electrons (or conduction electrons) move about the metal in a manner similar to that of gas molecules moving in a container 1

2 B. Insulators (also called Dielectrics): Materials in which all electrons are bound to the atoms and cannot move freely through the material. 1.3 Coulomb s Law (1785) Let q represent electric charge. The term point charge refers to a charged particle of negligible size. 1. The magnitude of the electric force exerted by charge q 1 on charge q a distance r away is F elec = k e q 1 r q Where k e = 8.99x10 9 N m /C Coulomb s constant Define another constant, called the permittivity of free space oin terms of Coulomb s constant k e as k e 1 = 4 " o Where o = 8.85x10-1 C /N m. The direction of the electric force e F depends on whether the charges attract or repel, and on which charge we calculate the force on.

3 Electric force is a vector quantity. The resultant force acting on an electric charge is equal to the vector sum of the forces exerted by the various individual charges (superposition principle). That is, F on1 = F on1 + F3 on1 + F4 on Electric Fields Electric fields E can be generated by Electric charges, either at rest or moving, and Time-varying magnetic fields (chapter 9) 3

4 A. Electric Fields generated by point charges q A point charge generates an electric field in the region of space around it. 1. The magnitude of the electric field E generated by a point charge q at a distance r away from it is given by E = k e r q. The direction of the electric field generated by a point charge is (a) away from the charge if the charge is positive 4

5 (b) toward the charge if the charge is negative. The unit of electric field in the metric system is the Newton per Coulomb. Electric field lines start at positive charges and extend out to either a negative charge or to infinity. 5

6 The E field vector is tangent to the electric field line. At any point P in space, the total electric field generated by a collection of point charges equals the vector sum of the electric fields generated at that point by the individual point charges (superposition principle). E at P = E1 + E + E

7 B. Electric Fields generated by continuous charge distributions 1. First define (a) charge per unit length as " # dq ds dq = " ds Q = # " ds Q = L if λ is uniform. (b) charge per unit area as dq " dq = da Q = da " da Q = A if σ is uniform. (c) charge per unit volume as dq " dq = dv Q = dv " dv Q = V if ρ is uniform. 7

8 . Then write down an expression for the electric field de generated at point P by an infinitesimal element of charge dq in the charge distribution at a distance r away from point P, i.e., ke dq de = rˆ r 3. Consider the symmetry of the charge distribution to see if any electric field components at the point of interest cancel out, 4. Finally, integrate the above expression to include the electric field contribution at the point of interest P due to all of the charge in the distribution. That is, E = k e dq ˆr r 8

9 Motion of Charged Particles in a Uniform External Electric Field What is the connection between electric force F and electric field E? Consider a point charge q located in a region of space where there already exists an external electric field E ext (generated by some other electric charge somewhere else). Then the force exerted by the external electric field E on the point charge q is given by ext F = q elec E ext In order to consider the motion of a point charged particle in an external electric field, then use Newton s Second Law of motion: F = m a q E ext = m a q a = E ext m The acceleration is constant if constant in time. E ext is uniform and 9