Maxwell’s Equations Electromagnetic In the electric field E, and the magnetic field B, a charge q will experience a force: the Lorentz force: F = q{E + v × B}. Static Charges produces E fields and Moving charges produces B fields

Maxwell’s Equations Electromagnetic The effects may be summarized in the expressions for the divergence and the curl of E and B: divE = /, curlE = 0 , divB = 0 , curlB = µ0J

Maxwell’s Equations Electromagnetic Equations without divergence and curl express passive aspects, while with curl and divergence express active aspects. A field with a curl but no divergence is called a solenoidal field, while one with a divergence but no curl is called an irrotational field.

Electrostatic Field Potential Distribution.

Equipotentials and Electric Field Vectors of Electrostatic Field Equipotentials and Electric Field Vectors of Electrostatic Field.

Electric Field Vectors Equipotentials and Electric Field Vectors of a Microstrip Line.

Potential Distribution Potential Distribution associated with a Corner Resistor.

Electric Field Magnitude Logarithmic scaled Electric Field Magnitude

Electrodynamics F = eE A Charged Particle If a charged particle is set free in an electric field, it is accelerated by a force proportional to the field and charged particle F = eE Where F is Force e is a charge, and E is electric Field Intensity

Electrodynamics d(mv) dv dm F = = m + v dt dt dt Newton’s Second Law Where m = mass of particle, kg V = velocity of particle, m-1

Electrodynamics F = m dv = ma dt ma = eE Newton’s Second Law F = m dv = ma dt ma = eE Velocity is very small as compared to velocity of light Mass is essentially constant

Electrodynamics W = m  a •dL = e E • dL W = m v •dv = eV Energy Integrating the force over the distance traveled by charged particle is 2 2 W = m  a •dL = e E • dL 1 1 While the Integral of E between points of 1 and 2 is a potential difference V 2 W = m v •dv = eV 1 W = ½ m( v22 – v12) = eV

Electrodynamics W = eV = ½ mv2 Particle Energy where W = energy acquired by particle, J v2 = velocity of particle at point 2, or final velocity, ms-1 V1 = velocity of particle at point 1, or initial velocity, ms-1 e = charge on particle, C m = mass of particle, kg V = magnitude of potential difference between points 1 & 2, V

Electrodynamics  =  2eV/m Final velocity Considering a charged particle e starting from rest and passing through a potential of V, will attain the final velocity of :-  =  2eV/m

m = mass of 0.91 x 10-30kg, will attain Velocity = v = 5.9 x 105 V Electrodynamics Final velocity While e = 1.6 x 10-19C falling through V = 1 volt Energy = 1.6 x 10-19 Joules m = mass of 0.91 x 10-30kg, will attain Velocity = v = 5.9 x 105 V at 1 volt the charge attains 590 kms-1

Electrodynamics ay = eVd eVdL ; vy = ayt = md mvxd vy ;  = tan-1 vx L Ed  vx d

Electrodynamics Problem:- A CRT with Va = 1500V, Deflecting space d = 10mm, Deflecting plate length = 10mm, Distance x = 300mm, Find Vd to deflection of 10mm:- Deflection y = VdLx/2Vad Vd = 2Vady/Lx= 100 V

Electrodynamics dF = (I x B)dL (N) …Motor equation I = q/t Moving particle in static magnetic field Force on a current element dL in a magnetic field is given by: dF = (I x B)dL (N) …Motor equation I = q/t IL = qL/t = qv IdL = dqv dF = dq(v x B) F = e(v x B) Lorentz force

Moving conductor in a magnetic field Electrodynamics Moving conductor in a magnetic field E = F/e = v x B V12 =  E • dL =  (v x B) • dL 2 2 1 1 1 Generating Equation B    dL   v          2 E = v x B

Electrodynamics Magnetic Brake

Electrodynamics Magnetic Brake I, B, & PUSH Therefore F due to I is opposing to PUSH Conductive Plate Magnet Assembly

Electrodynamics Magnetic Levitation

How does the LEVITRON¨ work? When the top is spinning, the torque acts gyroscopically and the axis does not overturn but rotates about the (nearly vertical) direction of the magnetic field.

How does the LEVITRON¨ work? levitionta

Electrodynamics levitation

Electrodynamics levitation "We may perhaps learn to deprive large masses of their gravity and give them absolute levity, for the sake of easy transport." - Benjamin Franklin

Electrodynamics Maglev Trains

Electrodynamics Maglev Train A maglev train floats about 10mm above the guidway on a magnetic field. It is propelled by the guidway itself rather than an onboard engine by changing magnetic fields (see right). Once the train is pulled into the next section the magnetism switches so that the train is pulled on again. The Electro-magnets run the length of the guideway

Electrodynamics Maglev Train Track

Maglev Train Aerodynamics Brakes

Electrodynamics no components that would wear out Advantages: no components that would wear out there is no friction. Note that there will still be air resistance. less noise The final advantage is speed