Magnetic Force on a Current-Carrying Wire
Magnetic force on a current-carrying wire is related to four variables – the strength of the magnetic field surrounding the wire, the amount of current flowing through the wire, the length of the wire and the angle between the magnetic field direction and the current direction. The formula that relates all these variables is:
F = BILsinθ
B = the strength of the magentic field in Teslas (T)
I = the amount of current flowing through the wire in Amperes (A)
L = the length of the wire in meters (m)
θ = the angle between B and I (notice that if the angle is zero, or the wire is parallel to the field, the resulting force is zero; if the wire is perpendicular to the field, the resulting force is at a maximum since the sine of 90 is equal to 1.)
Force, (as in every other case) ends up to be in Newtons (N).
The Right Hand Rule for Force on a Current-Carrying Wire
If you grab the current-carrying wire with your right hand, and point your thumb in the direction of the current, your fingers will point in the direction of the field and your palm will give the force direction. For example, for a wire lying in the plane of this page in the x-y direction with the current flowing east (to the right, +x), grabbing the wire will show your fingers coming out of the page on the top of the wire (+z for the field) and going into the page for the bottom of the wire (-z for the field). Your palm will face downwards (-y) for the force above the wire and face upwards (+y) for the force below the wire. This becomes especially important when you are dealing with two wires in the same field. (TRY THIS WITH A PENCIL AS THE WIRE.)
NOTE: If asked for the direction of the “electron flow”, remember that this is, by convention, opposite to the flow of the current. The current actually moves in the direction of positive charges. Some people use the left hand on the wire to give the direction of the electron flow, but you can still use the right hand, just reverse the direction of your answer.
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