This document presents Maxwell's equations in integral form. It summarizes: 1) The Maxwell equation ∇.D = ρ is expressed in integral form as the surface integral of D over any closed surface equals the volume integral of ρ over the enclosed volume. 2) The Maxwell equation ∇.B = 0 is expressed in integral form as the surface integral of B over any closed surface equals zero. 3) The Maxwell equation ∇ X E = - ∂B/∂t is expressed in integral form as the line integral of E around any closed loop equals the negative time rate of change of the surface integral of B over any surface bounded by the loop. 4)

1. JAI NAYAIN VYAS UNIVRSITY JODHPUR
ELECTRODYNAMICS AND PLASMA
PHYSICS
SEMINAR: 2022-23
SUBMITTED TO : - BHARAT PATEL
REPRESENT BY : - NARESH KUMAR

2. MAXWELL EQUATION IN
INTEGRAL FORM

3. MAXWELL EQUATION : -
a. ∇.D = ρ
b. ∇ .B = 0
c. ∇ X E = - მB/მt
d. ∇ X H = მD/მt + J

4. MAXWELL EQUATION IN
INTEGRAL FORM : -
a. ʃs D.ds = ʃv ρ dv
b. ʃs B.ds = 0
c. ʃ E.dl = - მ/ მt ʃs B.ds
d. ʃ H.dl = ʃs (J + მD/მt).ds

5. 1. ʃs D.ds = ʃv ρ dv
• We know that
∇.D = ρ (1)
• Apply volume integral both side
ʃv (∇.D)dv = ʃv ρ dv (2)
• Apply gauss divergence theorem
ʃv (∇.D)dv = ʃs D.ds { S.I. = V.I.} (3)
eqn (2) and (3)
ʃs D.ds = ʃv ρ dv H.P.

6. • We know that
∇ .B = 0 (1)
• Apply volume integral both side
ʃv (∇.B)dv = 0 (2)
• Apply gauss divergence theorem
ʃv (∇.B)dv = ʃs B.ds { S.I. = V.I.} (3)
eqn (2) and (3)
ʃs B.ds = 0 H.P.
2. ʃs B.ds = 0

7. • We know that
∇ X E = - მB/მt (1)
• Taking surface integral both side
ʃs (∇ X E ).ds = - მ/მt ʃs B.ds (2)
• Apply stokes theorem
ʃs (∇ X E ).ds = ʃl E.dl { L.I. = S.I. } (3)
eqn (2) and (3)
ʃ E.dl = - მ/ მt ʃs B.ds H.P.
3. ʃ E.dl = - მ/ მt ʃs B.ds

8. • We know that
∇ X H = მD/მt + J (1)
• Taking surface integral both side
ʃs(∇ X H ).ds = ʃs ( მD/მt + J).ds (2)
• Apply stokes theorem
ʃs(∇ X H ).ds = ʃl H.dl { L.I. = S.I. } (3)
eqn (2) and (3)
ʃ H.dl = ʃs (J + მD/მt).ds H.P.
4. ʃ H.dl = ʃs (J + მD/მt).ds

9. THANKYOU