Magnetic Force on a Current

• Consider a current-carrying wire in the presence of a magnetic field B.

• There will be a force on each of the charges moving in the wire. What will be the total force dF on a length dl of the wire?

• Suppose current is made up of n charges/volume each carrying charge q and moving with velocity v through a wire of cross-section A.

• Force on each charge =

• Total force =

• Current =

N

S

Yikes! Simpler: For a straight length of wire L carrying a current I, the force on it is:

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