From Flux Graphs to E.m.f. Graphs
From Flux Graphs to E.m.f. Graphs
- The induced e.m.f. comes from the gradient of a flux-linkage graph, not from its height.
Straight sections give constant e.m.f.
If the graph shows magnetic flux density and the coil's turns, area and angle remain fixed, multiply the field gradient by the constant factor . The graph and the flux-linkage graph then have the same shape.
- Split the input graph into sections with one clear gradient.
- A straight rising or falling section gives a constant e.m.f. A horizontal section gives zero.
- Opposite gradients give opposite e.m.f. signs. The chosen output polarity decides which sign appears above the axis.
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Recent marking awarded separate marks for the non-zero sections, flat tops, correct magnitude and opposite signs (9702/42/O/N/23 Q7(b)(ii)).
Common mistake
A flux-linkage graph is horizontal at a large positive value. State the induced e.m.f. and explain your answer.
Show worked answer
The induced e.m.f. is zero because the graph gradient is zero. The flux linkage is large but constant.
For a curve, use a tangent
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- A tangent gives the gradient at one instant. The steepest tangent gives the greatest e.m.f. magnitude.
- For sinusoidal flux, e.m.f. is zero at every flux maximum and minimum. Its magnitude is greatest at every zero crossing.
- The e.m.f. has the same period as the flux but is shifted by one quarter of a cycle.
A 2024 paper required the tangent at the steepest point, multiplication by 340 turns and the correct sinusoidal e.m.f. graph (9702/42/M/J/24 Q7(b)(ii)–(iv)).