Question

1. point charge equivalently show that the scalar potential and electric field of a moving with constant velocity a can be written Ver, t = t 9 - 4TE0 R (1-v²sn²0/0²) as Ecř, t) - Site ATTEO (1-r*sino/) / R = r _ vt

Answer 1

Potential from So frome in 12 no = ro (x + VC) = V kx үр - е VE Zo = Z = R2 Ř - Rait Ky ↑ + R2 Ê By wig can n eeter have along notation from abone figure with transformation equation 1- 4T to ( 82 R2 Costo + R² Sino) / 4 h to R (p2 Carlot Sim20)/ 47 € R (( - ) Cun'B + Sin?0) % . All the cutt Sumo ]" 4 T to R Con 20+ Sinzo - Go

4 T to R I (Cos²o + c2 sinon v2 Sino] / C2-01 4 TER 4TER 2 Sino 7 / - 4 T Go R 471 ( ORY

Electric field of a point charge motion. in uniform A point origin in to find the charge in at speed In so charge 9 de aut rest at the a dystern So. we are going entire tield & the came agstem s moves to the right v relative to s. the field in Er for me E = 4T to R² qko Exo - Ego a ATO uto [kel + y + 2007 % hit yox 2") % 970 Ezo - 572 4 T to Ho+ 21

- By ming transformation rule Et - Vect and NEM E" - E = (1 - 12 July Gebol - and 11 symbolices perpendale parallel component. The and parallel component. 9 No Ex Ex. 1 t (2249624 2073 Egr Ey. V9 yo 171 to 17 + 20 ) / Era X Ema Yato An (x²+ Yet z 12 so terms field wing of the point p. Lorentz Then are still expreens in Coordinates (co, to, 2) of the In terms of s trame, by transformation (invern): we get k = (x+vt) = V Rx yo - y - Ry 7.- 7 = Rz

P. Then, where, Ř in the rector from 9 to El rad 4T to (V2R²Cas²0 tR? Sino) / 4 82 4 TL to hooo to Do Ti ve siño 722 (2