Faraday’s Law: Coil Moving Through a Magnetic Field
Faraday's Law: Coil Moving Through a Magnetic Field
Move a rectangular coil into, through and out of a uniform magnetic field, and see how the flux linkage and the induced emf change, using ε = −NΔΦ/Δt
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Drag the time slider, or use the ◀ ▶ buttons to step through the motion. The times shown are the real times; the playback speed only changes how fast it plays on screen.
Live values
Think first: what happens to the flux linkage while the coil is completely inside the field? It is still moving, so is there still an emf?
Time
Area inside the field
Flux linkage, NΦ
Induced emf, ε
Stage
Working, stage by stage
Equations
Flux and flux linkage. The magnetic flux through a coil is Φ = BA, where A is the area of the coil that is inside the field, at right angles to it. Flux is measured in webers (Wb). For a coil of N turns, the flux linkage is NΦ = BAN, measured in Wb turns.
Entering the field. As the coil moves in at a steady speed, the area inside the field grows at a steady rate, so the flux linkage rises in a straight line. A steady rate of change of flux linkage means a constant induced emf.
Fully inside. Once the whole coil is in the uniform field, the flux linkage stays the same even though the coil is still moving. No change in flux linkage means no induced emf.
Leaving the field. The area inside the field now shrinks at a steady rate, so the flux linkage falls in a straight line. The emf has the same size as when the coil entered, but the opposite sign.
Faraday's law and Lenz's law. The induced emf equals the rate of change of flux linkage, ε = −NΔΦ/Δt. The minus sign comes from Lenz's law: the induced current flows in the direction that opposes the change that caused it. So the emf graph is the gradient of the flux linkage graph, turned upside down.
A useful link. While one edge is crossing into the field, the area changes at a rate Lv, so the size of the emf is BLvN. The area under each block of the emf graph equals the change in flux linkage, BAN.
