In classical electromagnetism, we separate the electric field E and the magnetic field B. If we isolate E, we get rest: electrostatics. Charged particles exert

In classical electromagnetism, we separate the electric field E and the magnetic field B. If we isolate E, we get rest: electrostatics. Charged particles exert an attractive or repelling force in proportion to their charge, just like gravity, except charge instead of mass. So E is time-symmetric. This applies to your example. Now consider just B. A positively charged particle is moving to the left, through a magnetic field that points inwards. By the right-hand rule, the force on the particle is up. Reverse time: now the particle is moving to the right, so you rotate your hand 180 degrees and the force is downwards. This magnetic field produced an upwards force forwards in time and a downwards force backwards in time: it's antisymmetric. Put mathematically we have: F = qv x B where q is the charge, v is the velocity, B is the field. Reverse time and the velocity gets a minus sign, so F reverses. So E is symmetric and B is anti-symmetric.