lecture 4

Lecture 4
GAUSS S LAW This law states that the total electric flux ? through any closed surface, or (equivalently) the surface integral over the normal component of the electric field vector E over that closed surface, equals the net charge ?_n?q_n inside the surface:
?=???E.dS?=1/?_o ?_n?q_n =1/?_o ?_V??dV …. (1-8)
where dS is the surface element vector at any point p on the surface surrounding the volume V. If the charge is distributed within the volume, ? is the localized charge density within a volume element dV. This law can be expressed in differential form as
??D=? …… (1-9) (how?)
This is considered the first of Maxwell s equations.
BIOT-SAVART LAW
B=?_o/4? ?_V??J(V)×r/|r|^3 dV? …….. (1-10)
where J(V) is the current density within volume element dV and r is the position vector from volume element dV to the point of measurement of B. It can be expressed in differential form as:
B=?_o/4? ?×???(J(V))/|r| dV? …….. (1-11)
which leads directly to:
??B=0 ………. (1-12) (How?) (Prove it)
since B is the curl of another vector. This is considered the second of Maxwell s equations.

GAUSS S LAW This law states that the total electric flux ? through any closed surface, or (equivalently) the surface integral over the normal component of the electric field vector E over that closed surface, equals the net charge ?_n?q_n inside the surface:
?=???E.dS?=1/?_o ?_n?q_n =1/?_o ?_V??dV …. (1-8)
where dS is the surface element vector at any point p on the surface surrounding the volume V. If the charge is distributed within the volume, ? is the localized charge density within a volume element dV. This law can be expressed in differential form as
??D=? …… (1-9) (how?)
This is considered the first of Maxwell s equations.
BIOT-SAVART LAW
B=?_o/4? ?_V??J(V)×r/|r|^3 dV? …….. (1-10)
where J(V) is the current density within volume element dV and r is the position vector from volume element dV to the point of measurement of B. It can be expressed in differential form as:
B=?_o/4? ?×???(J(V))/|r| dV? …….. (1-11)
which leads directly to:
??B=0 ………. (1-12) (How?) (Prove it)
since B is the curl of another vector. This is considered the second of Maxwell s equations.