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Induced emf calculator

A-level Electricity

Faraday’s law: the size of the induced emf equals the rate of change of flux linkage.

ε = N ΔΦ / Δt

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

1.20 V

Working

  1. Write the equation
    ε = N ΔΦ / Δt
  2. Substitute the values
    ε = 200 × 0.003 ÷ 0.5
  3. Calculate
    ε = 1.2 V
  4. Give the answer to 3 significant figures
    ε = 1.20 V

Worked example

Find ε, the induced emf (size). Given: number of turns N = 200; change in magnetic flux ΔΦ = 0.00300 Wb; time taken Δt = 0.500 s.

  1. Write the equation
    ε = N ΔΦ / Δt
  2. Substitute the values
    ε = 200 × 0.003 ÷ 0.5
  3. Calculate
    ε = 1.2 V
  4. Give the answer to 3 significant figures
    ε = 1.20 V

Symbols and units

SymbolQuantitySI unit
εInduced emf (size)V
NNumber of turnsno unit
ΔΦChange in magnetic fluxWb
ΔtTime takens

Induced emf: rearranged

  • To find induced emf (size): ε = N ΔΦ / Δt
  • To find number of turns: N = ε Δt / ΔΦ
  • To find change in magnetic flux: ΔΦ = ε Δt / N
  • To find time taken: Δt = N ΔΦ / ε

Exam tip

The minus sign in Faraday’s law (Lenz’s law) gives the direction of the emf. This calculator gives the size.

Common questions

What is the formula for induced emf?

The equation is ε = N ΔΦ / Δt, where ε is the induced emf (size) (V); N is the number of turns; ΔΦ is the change in magnetic flux (Wb); Δt is the time taken (s).

What units should I use for induced emf?

In SI units: induced emf (size) in V, number of turns in no unit (a ratio), change in magnetic flux in Wb, time taken in s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange ε = N ΔΦ / Δt?

Rearranging gives these forms: to find induced emf (size): ε = N ΔΦ / Δt. to find number of turns: N = ε Δt / ΔΦ. to find change in magnetic flux: ΔΦ = ε Δt / N. to find time taken: Δt = N ΔΦ / ε.

Practise induced emf questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

More electricity equations: Charge, current and time, Ohm’s law, Electrical power, Electrical power, Energy transferred, Resistors in series, Resistors in parallel, Resistivity. See the full list on the a-level physics equation calculator page.