Electromagnetism 2004 Fall Zhang Yang Dept. Astron. appl. phys Reference K Electromagnetism, principles and application》 by plorrain d Corson
Electromagnetism 2004 Fall Zhang Yang Dept. Astron. & Appl. Phys Reference: 《 Electromagnetism, principles and application》, by P.Lorrain & D.Corson
Chapter 2 Fields of Stationary Electric Charges Coulombs Law Electric Field intensity E Superposition and Extented Charge Distribution Electric Potential Electric dipole
Chapter 2 Fields of Stationary Electric Charges ◼ Coulomb’s Law ◼ Electric Field Intensity E ◼ Superposition and Extented Charge Distribution ◼ Electric Potential ◼ Electric Dipole
2 1 Coulomb's law Given two stationary point charges @a and Qb, it is experimentally found that the force exerted by a on 1 aqb ab r 丌∈0 where ri is a unIt vector pointing in the direction trom Qa to Qb, and the permittivity of free space(vacuum) 0=8.85187817×10-12 farad/ meter Interpretation
Q Figure 2-1 Charges 2, and 2, separated by a distance r. The force exerted on go by 2 is Fe and is in the direction of r, along the line joining the two charges
Explanation (1) the force acts along the line joining the two charges, in the direction r1 (2 the force is o the product QaQb, so the force is repulsive if Qa & qb are of the same sign attractive if Qa&@b are of the different sign (3 the force x r important.(what if not Unit:(in SI Unit System Fab-- newton; a Abcoulomb; r-meter
enormous magnItude b≈9×100a6, while the gravitational force btwn masses ma and mb b=667×10-1020 For instance, two protons (Q=e=1.6x 10-C, mp=1.67 x 10-kg )at a distance of one meter Coulomb force: Fn10-28N gravitational force: FN 10-DN The Coulomb force is roughly 106 times greater than the gravitational force But, we have experienced much more influence of gray ity than Coulomb force Why? The Universe is presumedly neutral-cosmology
2.2 The electric field intensity e Definition: the electric field intensity due to the point charge cla is ab b2623 Explanation (1)it's the force exerted on a unit test charge; (2 )E has a unit volt/meter ( Ea is a vector field over the whole space (4)a exists as long as @a is present, regardless of Important (5)It' very simple to get the force acting on Q FEQE
2. 3 The principle of superposition If more than one charge are dis ibuted each generates a field e The resultant E is simply the vector sum of individual (r)=∑E2 Q r-r 2士丌enr-r where (r-ri)l is a unit vector pointing trom ri to. This is called the principle of superposition Explanation: (1) experimentally set up (2)theoretically, the Maxwell theory(equations )is a linear theory; so electromagnetism is easy to study, in comparison with other fundamental forces
Figure 22 Source point (x, y, = )in a charge distribution and field point (x, y,=)
Fields of an extended charge distribution a general distribution of charges in space is usually describec by an electric charge density pl Once p(r) is given, one can calculate the electric fiel e(r) generated E(r\=>Ei +TE0r-r2-I)idr Remarks (1)Application of this expression to get e is techni- cally more complicate, since it involves a summation of vectors (2)There is another way to obtain E more efficiently (thru V)