Magnetic Flux, Flux Linkage and Faraday's Law
For a uniform field, flux through a flat loop is B A cos theta, with theta measured from the loop normal. Flux linkage is N times the flux. Signed induced emf is the negative rate of linkage change; its magnitude is the absolute value.
What a learner can do afterwards
- Calculates flux as BA cos theta and flux linkage as the number of turns times the flux
- Finds signed induced emf from the negative gradient of a flux linkage against time graph, and emf magnitude from the gradient's absolute value
- Explains why a coil turning in a steady field still has a changing linkage
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Induction produces an emf (voltage) when flux linkage changes. In a uniform field, a flat loop has flux B A cos theta. Theta is the angle between field and loop normal, perpendicular to the loop. Flux is in webers: 1 Wb = 1 T m squared. Face on, theta = 0 and cos theta = 1. Edge on, theta = 90 degrees gives zero flux even in a strong field. For N turns sharing the same flux, linkage is N times flux, in weber-turns.
Average emf = -(change in flux linkage)/(elapsed time). Instantaneous emf is the negative gradient of a linkage against time graph. An emf's magnitude is its absolute value; a flat line gives zero emf. With fixed reference directions, the minus sign follows Lenz's law: the induced effect opposes the flux change. A straight fall from 10 to 2 weber-turns in 4 s gives gradient (2 - 10)/4 = -2 Wb/s and emf +2 V.
A coil turning so that the angle between its normal and a steady field changes has changing flux linkage. Linkage is N B A cos theta; with N, B and A fixed, changing cos theta changes linkage. A rotating-coil generator uses this effect. Faster rotation, more turns, a stronger field or a larger coil area increases the peak emf for this arrangement, with the other quantities fixed.
Flux = B A cos theta; linkage = N times flux. Emf is the negative rate of linkage change, and its magnitude is the absolute value. A rotating coil can keep linkage changing.
Original magnetic-flux lesson and questions written for Marble.
Original magnetic-flux readings and flashcards written for Marble. Linked videos are by Khan Academy India - English and Khan Academy; their licenses are unknown.
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