Topic 4 of 9
Force on a current-carrying conductor
A magnetic field can exert a force on a current-carrying wire. Find its magnitude from the active length and angle, and its direction from the field and conventional current.
For a straight conductor with length l inside a uniform external field B, carrying current magnitude I:
The angle θ is between current and B. The active length l is the part in the field, not automatically the entire wire. Use the field produced by the magnet or another source; do not treat the wire's own field as though it pushes the wire sideways by itself.
Perpendicular current gives the maximum BIl. A conductor parallel or antiparallel to B gives zero magnetic force because sin θ = 0. A current-carrying conductor can therefore be in a nonzero field without experiencing a magnetic force.
Use Fleming's left-hand rule
Hold the left thumb, first finger and second finger mutually perpendicular. The first finger is field, the second is conventional current and the thumb is force on the conductor. If current is not perpendicular to B, use its perpendicular component for the direction rule; the sine factor supplies its magnitude.
For current right and B into the page, force is up. Reversing either current or field reverses the force; reversing both restores it. For current up and B right, the force is into the page. Name the selected conductor: the magnet's opposite reaction acts on a different body.
Perpendicular current: the wire force is upward
Brown: conventional current. Teal crosses: external B into the page. Purple: magnetic force on the chosen wire. The field, current and force use separate schematic arrow scales.
Parallel current and field: no magnetic force
A current can be present while magnetic force is zero. Parallel and antiparallel orientations both give sin(theta) = 0.
A real 30-degree angle in the page
This is a different physical orientation from the first panel. The angle is between I and B. Their cross-product direction gives force out of the page, and sin(30 degrees) halves the force magnitude.
Calculate and check the scale
A rough B of 0.1 T, I of 2 A and active length of 0.1 m suggest a perpendicular force around 0.02 N. For the supplied precise model, B = 0.0800 T into the page, I = 2.50 A right and l = 0.120 m:
Now consider the separate arrangement with the same magnitudes and an actual 30.0° angle between current and B:
= 0.0120 N
In its shown view, B is up and current is 30.0° to the right of up, so the force is out of the page. An in-page arrow cannot make a 30° angle to a field directed straight into the page; those directions would be perpendicular.
Define magnetic flux density
Magnetic flux density is the force per unit current per unit length on a straight conductor placed perpendicular to the field:
1 T = 1 N/(A m) = 1 kg s-2 A-1
One tesla gives 1 N on a 1 m perpendicular active length carrying 1 A. Without the perpendicular condition, F/(Il) would give B sin θ instead of B. A field value in teslas is not a force until the current, active length and orientation are known.