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Question:

How strong of a force does a magnetic field exert on metal when it passes through the field?

When non magnetic metal (like a plate with fins) passes through a magnetic field there is a resistance which slows down the plate, I am wondering how strong that resistance is and how you would analyze that force.

Answer:

It's eddy current damping, and is proportional to the speed of plate movement. Basically the plate is a series of short-circuited coils which generate circulating currents which generate magnetic fields opposing the motion, not unlike a shorted generator. Since the current increases as the conductivity of the plate does, it's especially noticeable with thick plates of copper and aluminum. (You don't want magnetic materials like iron because the magnetic force will interfere with isolating and feeling the damping force.) When damping force is proportional to velocity it's often called viscous damping, which is just how it feels, like the plate is immersed in honey. Both references below give formulas that boil down to: F Vol*vB^2σ, where Vol is the volume of material that is in the magnetic field, v is velocity, B is magnetic field, and σ is volume conductivity of the material (inverse of volume resistivity).
You need some data in order to calculate a force. Preferably teslas of field, velocity of plate and coulombs of plate.

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