Force on a current-carrying wire
Electric current is the charge that passes through the normal section S of a conductor per unit time. In the study of the ionic engine we saw the meaning of mass flux and charge flux or electric current
Then the charge Q that passes through the normal section S in a time t, is that contained in a cylinder of cross section S and length v·t.
Charge Q= (number of particules per unit volume n)·(charge of each particle q)· (volume of the cilinder Svt)
Dividing Q by the time t we obtain the electric current.
The electric current is the flux of charge or the charge that passes through the normal section S per unit time, which is the product of the following terms:
The figure shows the direction of the force that exerts the magnetic field B on a positive charged particle q, which moves towards the left with velocity v.
Let us calculate the force on all the charged (nSL) particles contained in the current-carrying wire of length L.
The unit vector ut=v/v has the same direction as the velocity vector, or the direction in which the positive charged particles move.
In the case of a non-straight current-carrying wire, or a non-constant magnetic field, one has to calculate the force on an element of current dl
To show the force that exerts a magnetic field on an electric current we build a device that consists of a powerful magnet which produces a field of 500 gauss or B=0.05 T, and on its north pole we stick two rails made with copper sheets. The conducting segment is a copper wire of length L=15 cm.
The current is supplied by an arc discharge of i=60 A. As the electric current and the field are perpendicular, the force on the wire will be
If the mass of the wire is 1.35 g, the acceleration will be 333.3 m/s2. The large accelerations obtained could suggest the use of the wire as the projectile of an electromagnetic canon.
The velocity of the wire at the end of the 50 cm-long rails is
You can vary
Press the Start button ,
Observe the movement of the wire. At the top of the applet, you can see the position and velocity of the wire as a function of time.
By pressing the Pause button, you can stop the movement and see the field vector B, the direction of the current, and the force vector F on the wire. To resume the movement of the wire, press the same button which is now labelled Resume.