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Unformatted text preview: Lorentz Transormation: ! x = " ( x # vt ) ! y = y ! z = z ! t = " ( t # vx / c 2 ) Inverse Lorentz Tranformation: x = ! ( " x + v " t ) y = " y z = " z t = ! ( " t + v " x / c 2 ) Relativistic transformation of velocities ! u x = ( u x " v ) / (1 " u x v / c 2 ) ! u y = u y / # (1 " u x v / c 2 ) Inverse Transformation: u x = ( u x + v ) / (1 + u x v / c 2 ) u y = u y / (1 + u x v / c 2 ) Relativistic Doppler Effect: f obs = 1 + v / c 1 ! v / c f source ( approaching ) Relativistic Momentum p x = ! mu x ; similarly for y- and z-components = 1 1 u 2 / c 2 Kinetic Energy K = mc 2 mc 2 Total Energy E = ! mc 2 = K + mc 2 E 2 = p 2 C 2 + M 2 C 4 Force due to Electric field : F = q E Force due to Magnetic Field: F = q vxB Particle of charge q moving in magnetic field B in circle of radius r has relativistic momentum P = qBr Stefans Law e t = ! T 4 = 5.67.10-8 Wm-2 K-4 Plancks Blackbody radiation formula: u ( f , T ) df = 8 !...
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- Spring '09