Imagine you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally from back wall towards the from wall, is deflected by a strong magnetic field to your right side. What is the direction of the magnetic field?
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The direction of the magnetic field is vertically downwards. The direction of current is from the front wall to the back wall because negatively charged electrons are moving from back wall to the front wall. The direction of magnetic force is rightward. Hence, using Fleming's left hand rule, it can be concluded that the direction of magnetic field inside the chamber is downward.