Begin2.DVI

Note 2: The product μ 0

0 =^1

c^2

, where c= 3 ×(10)^10 cm/sec is the speed of light.

It will be demonstrated later in this chapter that the vector fields describing E

and B of Maxwell equations are solutions of the wave equation.

Electrostatics

Coulomb’s law^9 states that the force on a single test charge Qdue to a single

point charge qis given by

F=

1 4 π 0

qQ r^2

ˆer (9 .135)

where

0 = 8. 85 × 10 −^12 coul

2

N·m^2

is the permittivity of free space, r is the distance

between the charges and ˆer is a unit vector along the line connecting the charges.

If q and Qhave the same sign, the force is a repulsive force and if qand Qhave

opposite signs, then the force is attractive.

If there are many charges q 1 , q 2 ,... , qnat distances r 1 , r 2 ,... , r nfrom the test charge

Qat the point (x, y, z ), then one can use superposition to calculate the total force

acting on the test charge. One finds

F=F(x, y, z ) =

∑n

i=1

Fi= 4 π ^1 0

( q 1 Q r^21 ˆer^1 +

q 2 Q r^22 ˆer^2 +···+

qnQ r^2 n ˆern

) =QE (9 .136)

where ˆeri, for i= 1,... , n , are unit vectors pointing from

charge qi to the point (x, y, z)of the test charge Q. The

quantity

E=E(x, y, z) =^1 Q

F(x, y, z ) =^1 4 π 0