Imrana Ashraf Zahid Quaid-i-Azam University Islamabad Pakistan Preparatory School to Winter College on Optics: Light : A Bridge between Earth and Space. 2nd February - 6th February 2015 Electrostatic : Revisited ¨  Magneto- static : Revisited ¨  Introduction to Maxwell’s equations ¨  Electrodynamics before Maxwell ¨  Maxwell’s correction to Ampere’s law ¨  Maxwell’s equations in vacuum ¨  Maxwell’s equations inside matter ¨  The Electromagnetic wave in free space ¨  29-Jan-15 2 E = Electric field ¨  D = Electric displacement ¨  B = Magnetic flux density ¨  H = Auxiliary field ¨  ρ= Charge density ¨  j = Current density ¨  µ (permeability of free space) = 4π×10-7T-m/A ¨  0 ε (permittivity of free space) = 8.854×10-12N-m2/ ¨  0 C2 c (speed of light) = 2.99792458×108 m/s ¨  29-Jan-15 3 Electrostatics ¨  §  Electrostatic field : Stationary charges produce electric fields that are constant in time. The theory of static charges is called electrostatics. Stationary charges Constant Electric field; 29-Jan-15 4 Coulombs Law Q r 1 qQ Test F rˆ Charge = q 2 4 r πε 0 Source Charge 2 C ε = 8.85×10−12 Permittivity of free space 0 2 N − m 29-Jan-15 5 y F = QE r q q i P 2 1 n q i q Field E(P) = ∑ i rˆ n ʹ′ Point 2 i r 4πε r i r 0 i=1 i E x - the electric field of the source charges. Physically E(P) Is force per unit z charge exerted on a test charge placed at P. 29-Jan-15 6 P r 1 rˆ E(P) = ∫ λdl 2 4πε r 0 Line λ is the line charge density P r 1 rˆ E(P) = ∫ σda 2 4πε r 0 Surface σ is the surface charge density 29-Jan-15 7 P r 1 rˆ E(P) = ∫ ρdτ 2 4πε r 0 Volume ρ is the volume charge density 29-Jan-15 8 The work done in moving a test charge Q in an electric field from point P to P with a constant speed. 1 2 W = Force • dis tan ce P 2 W = − ∫ QE • dl p 1 negative sign - work done is against the field. For any distribution of fixed charges. ∫ E • dl = 0 The electrostatic field is conservative 29-Jan-15 9 Stokes’s Theorem gives E 0 ∇ × = E V = −∇ where V is Scalar Potential The work done in moving a charge Q from infinity to a point P where potential is V 2 W QV = V = Work per unit charge = Volts = joules/Coulomb 29-Jan-15 10