# Magnetic field in the moving inertial and noninertial reference frame

Physics Asked on May 8, 2021

Is there any generic way to calculate magnetic field in the moving inertial and noninertial reference frame?

For example, there is the Earth magnetic field, we can assume it is uniform permanent field. Let say approximately $$50mu T$$ (microTesla). If I am driving the car with 100km/h and have magnetic sensor what it will show? And if I accelerate in my car with acceleration $$2frac{m}{s^2}$$ what will my sensor in the car show?

I tried it with smartphone sensor and magnetic field increased 2-4 times while accelerating. I am just wondering if it is really true or it just my phone cheap sensor?

First off you need to be careful what you mean by inertial frames which can be from classical Newtonian view or Einsteinian general relativity view. First classically the inertial frames are the Cartesian systems where f=ma holds basically. You can boost from one to another with a uniform velocity transform. Now we often assume the ground or lab is such though this is a good approximation neglecting earth rotation. An accelerating or rotating frame will not uphold f=ma and we get fictitious forces like centrifugal or g forces in accelerating car. Earth surface already moves at near 1000 km/ hr. I don’t think this changes observer magnetic field much. Such alterations as usual are of order v/c squared where v is the speed in question and c the speed of light. Electromagnetism is already relativistic so Einstein tells the same as Maxwell electrodynamics anyway. Even for earth surface v/c= is very very small consider light would encircle the earth 7.5 times per second at equator ...Superman Film showed this! So v/c squared even smaller. Very interesting that your experiment shows some effects! Need to do these again and be a good detective, maybe some metal thing moved when you accelerated? Interesting question and experiment imo.

Answered by blanci on May 8, 2021

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