# Faraday's Law

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## Faraday's Law

**For a conductor in a changing magnetic field, the factors affecting the size of the induced emf are:**

- How quickly the magnetic field is changing;
- The number of turns or loops of the conductor in the field.

This leads to **Faraday's Law,** which is that:

**The emf induced is equal to the rate of change of magnetic flux linkage or the rate of flux cutting**

A plane of wingspan 30m flies through a vertical field of strength 5 x 10^{-4}T. Calculate the emf induced across wing tips if its velocity = 150ms^{-1}.

*Answer:*

Calculate the area swept out each second by the wings. Multiply that by the field strength, B and you have got the flux swept out in a second.

So each second, 2.25Wb of flux is swept out.

This method leads us to a simpler equation for the emf induced by flux cutting:

**E = Blv**

*Where:*

**B** = magnetic flux density, T

**l** = length of the conductor cutting the field, m

**v** = speed at which the conductor cuts the field, m/s

** Remember:**it is only the motion perpendicular to the field that induces an emf.

A coil of wire of area 2 cm^{2}, with 20 loops is situated in a magnetic field. The magnetic field changes from 20 T to 10 T in 2 seconds.

**What is the emf induced in the coil of wire?**

*Answer:*

= 0.02V

**What happens if a coil is rotated in a magnetic field?**

If a coil is spun in a magnetic field, the flux through the coil changes like this graph.

The flux through the coil is greatest when the coil is perpendicular to the filed and zero when the coil is parallel to the field. If the coil keeps spinning the flux varies like a sine curve.

** Note:** Magnetic field must be

**changing**to induce an emf. When the gradient of the magnetic field graph is zero (for instance, at the top of the peaks and bottom of troughs)

**the magnetic field is not changing so no emf is induced**- check the graph.

The magnetic field is changing most rapidly at the steep bits of the graph when it crosses the x-axis. These produce maximum values of emf.

So the magnetic field and induced emf are 90° or π/2 radians out of phase (out of step). This principle is used in an alternator - a generator of alternating current.

**If you move a conductor through a magnetic field, you always induce an emf!**

If there is a **circuit** available, the emf will push a current through it.

If there is **no circuit** you will still get an emf, but you won't get a current.