Page:Electricity (1912) Kapp.djvu/154

150 The force acts at right angles to the plane of the circular loop. A unit pole will therefore be drawn through the loop with the force

$$B = \frac{2\pi J}{R}$$

By means of this formula we may now define unit current. If $$J = 1$$ and $$R = 1$$, then $$B = 2\pi$$. Now imagine a wire bent into a circle of 1 cm. radius. If unit pole in the centre of this circle is drawn through it with a force of 6.28 dynes, then there is unit current in the wire. This so-called electromagnetic unit of current strength is too large for practical work, and for this reason a unit ten times smaller is adopted. This is called the ampere.

The coil exerts a force $$F = \frac{2\pi Jm}{R}$$ dynes on the magnetic mass $$m$$ placed in the centre of its plane, but since action and reaction must always be equal, this is also the force with which the mass $$m$$ acts on the wire. The induction due to $$m$$ in the space occupied by the wire is $$B = \frac{M}{R^2}$$, and by combining the equations for $$F$$ and $$B$$ we find $$F = 2\pi RJB$$ dynes.

This is the force experienced by a wire of