Begin2.DVI

If the discrete number of n-charges q 1 ,...,qnwere replaced by a continuous dis-

tribution of charges inside the surface, then the right-hand side of equation (9.141)

would be replaced by

∫∫∫

V

ρ


 0

dV where dV is an element of volume

(

meter^3

)

and ρ

is a charge density

(

coulomb

meter^3

)

and the equation (9.141) would then be written

∫∫

S

E·dS=

∫∫∫

V

ρ


 0 dV (9 .142)

Using the divergence theorem of Gauss, the equation (9.142) can also be expressed

as ∫∫

V

(

∇·E−

ρ


 0

)

dV = 0 (9 .143)

If the equation (9.143) is to hold for all arbitrary simple closed surfaces, then one

must require that

∇·E = ρ


 0

(9 .144)

This is the first of Maxwell’s equations (9.134) and is called the Gauss law of elec-

trostatics.

Magnetostatics

A moving charge produces a current and a moving

current produces a magnetic field. Consider a current

moving along a wire considered as a line. The magnetic

field created is described by circles around the wire.

The strength of the magnetic field falls off as the per-

pendicular distance from the line increases. One can

use the right-hand rule of letting the thumb point in

the direction of the current flow, then the fingers of the

right-hand point in the direction of the magnetic field

lines.

The magnetic force on a charge Qmoving with a velocity v in a magnetic field

B is given by

Fm=Q(v ×B) (coul)

(m

s

)( N

amp ·m

)

(9 .145)