Magnetic Flux Density and the Force on a Current-Carrying Wire
The strength of a magnetic field is defined by the force it produces: F = BIL when the wire is at right angles to the field, and BIL sin theta otherwise. One tesla is one newton per amp per metre.
What a learner can do afterwards
- Uses the left hand rule to give the direction of the force on a current-carrying wire
- Calculates the force for a wire set at an angle to the field and says when it becomes zero
- Defines the tesla from the defining equation rather than quoting it from memory
1 · Read
Use F = B I L sin theta to calculate the motor effect. F is force, B field strength, I current and L wire length in the field. Theta is the wire-field angle. In degree mode, sin 0 = 0 and sin 90 = 1. Multiply these factors. With B, I and L fixed, force is largest at 90 degrees and zero when parallel.
A 20 cm wire carrying 4 A at right angles to a 0.25 T field feels a force of 0.25 times 4 times 0.2, which is 0.2 N. Convert centimetres to metres first. Motors use loops of wire so that this push turns a coil.
The direction comes from Fleming's left hand rule. Hold the thumb, first finger and second finger at right angles. Point the first finger along the field and the second finger along the conventional current, and the thumb gives the force. Use conventional current, since electron flow points the other way and would flip the answer.
At right angles, F = B I L, so B = F/(I L): divide force by current times length. One tesla gives one newton on one metre carrying one amp, or one newton per amp per metre. Current is charge per second, not charge alone. Keep both I and L in the denominator.
Size comes from B I L sin theta, and direction from the left hand rule.
Original wire-force lesson and questions written for Marble.
Original wire-force readings and flashcards written for Marble. The linked video is by Khan Academy India - English; its license is unknown.
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به انگلیسیTake it off screen
Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.