Electromagnetism 2004 Fall Zhang Yang Dept. Astron. appl. Phys Reference K Electromagnetism, principles and application》 by p.lorrain 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 Coulomb' s 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 Qa and qb, it is experimentally found that the force exerted by la on 1 OO r 丌∈0 where ri is a unit vector pointing in the direction from Qa to Qb, and the permittivity of free space(vacuum) 0=8.854187817×10-12 arad/meter nterpretation
Figure 2-1 Charges Q, and @, separated by a distance r. The force exerted on Q, by 2, is F 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 @a&@b are of the same sign attractive if @a&@b are of the different sign (3 the force x r, important.(what if not Unit: (in SI Unit System) ab- newton; @a Qb-coulomb; r--meter
enormous magnitude Fn≈9×10 Qaq r while the gravitational force btwn masses ma and mb lamb=6.67 X 10-11mam 2 For instance, two protons(Q=e=1.6x 10-C, mp=1.67x10kg )at a distance of one meter Coulomb force Fo10-28N gravitational force: F N 10-N The Coulomb force is roughly 1036 times greater than the gravitational force But, we have experienced much more influence of grav 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 Qa is ab Q2 ar. Qb4m∈0r Explanation (1)it's the force exerted on a unit test charge; (2)E has a unit volt/meter (3)Ea is a vector field over the whole space; (4 )Ea exists as long as Qa is present, regardless of Qb(important) (5)It' very simple to get the force acting on Q F=QE
2. 3 The principle of superposition If more than one charge Qi,(i= 1, 2 …)are tributed each generates a field e The resultant e is simply the vector sum of individual E Q2 E(r)=2Ei 24丌or-;/2(r-ri)1, where(r-rill is a unit vector pointing from ri to r This is called the principle of superposition Explanation 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
x,y2) Figure 2-2 Source point (x', y, = )in a charge distribution and field point (x,y,l
Fields of an extended charge distribution a general distribution of charges in space is usually described by an electric charge density p(r) Once p(r) is given, one can calculate the electric field regenerated ATE0r-re(r-ridr E(r)=∑E2=1 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)