An observer standing by the railroad tracks sees two bolts of lightning strike the ends of a 500-m-long train simultaneously at the instant the middle of the train passes him at 50 m/s. Use the Lorentz transformation to find the time between the lightning strikes as measured by a passenger seated in the middle of the train.

PHYS 242 BLOCK 2 NOTES Sections 23.1 to 23.5 → Rewriting GeneralPhysics I’s Eq. (6.14) as Eq. (23.1), the wora→b done by a force F in moving a b ⌠ b particle from pointa to pointb is defined toa→bW≡ F·dl = ⌡F cos φ dl . a a If the force is conservatia→bW= U a U ,bwhereU is the potential energy associated with that force. b ⌠ If we have a test chargeq outside a spherically-symmetric, same-sign chargeq,= F·dl = 0 a→b a b 1 qq0 ⌡F cos φ dl , whereF =4πε0 r2 and dl cos φ = dr (see Fig. 23.6).Then integrating aromb to r gives us a 1 qq 0 1 qq 0 1 qq 0 4πε0 ra – 4πε0r b = Ua– U b Thus the simplest choice for the potential energy expression 4πε 0 r . This equation also holds for opposite-sign charges. Any equation in this block cε0