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Main >> Applications >> Sample problems >> Faraday's law of electromagnetic induction

This example demonstrates the appearance of a current in a closed coil when a permanent magnet is moved into the coil.

**Task type:**

An axisymmetric problem of transient magnetics.

**Geometry:**

**Given:**

The coil contains 200 turns of a 0.25 mm² wire.

Permanent magnet coercive force *H _{c}* = 500 kA/m.

Magnet motion speed

**Task:**

Calculate the induced current in the coil as a function of time (permanent magnet position)

**Solution:**

To simulate the motion of a magnet, the coercive force is represented by a formula of coordinates (*x*) and time (*t*).
*Hc**impulse(*x* + *v**(*t*-1.02)*step(*t*-1.02),0.08,0.1)

The *impulse* function describes the spatial pulse along the *x* axis in the range from 0.08 m to 0.10 m (the pulse spatial length 20 mm is equal to the axial length of the permanent magnet).

The pulse moves in space with a speed *v*.

Transient problem uses zero magnetic flux density distribution as the initial condition. Suddenly permanent magnet appears and causes the magnetic field distortion. It takes time for the disturbances caused by the appearance of the magnet to calm down. Therefore, we delay the motion start for a period of 1.02 s The delay is implemented by the *step* function.

You can study the function behavior in details using QuickField formula plotter online tool.

**Result**

Graph of current dependence and flux density distribution for specific moments of time.

Reference: Wikipedia: Faraday's law of induction.