A-level Physics (Advancing Physics)/Flux

A coil of wire creates magnetic flux. The amount of magnetic flux created depends on three things: the number of coils in the wire, the amount of current flowing through the wire, and the permeance of the object through which the flux is flowing. So:

$$\Phi = \Lambda NI$$,

where &Phi; is flux (in webers, denoted Wb), &Lambda; is permeance (in WbA−1) and I is current (in A). This is the total flux induced. NI is the number of "current-turns". Permeance is related to permeability (a material property) by the following equation:

$$\Lambda = \frac{\mu A}{L}$$,

where &mu; is permeability, A is cross-sectional area, and L is length. A permanent magnet is just like a coil, except that a current does not need to be generated to maintain the flux. Over smaller areas, we need to know the flux density B. This is the amount of flux per. unit area:

$$B = \frac{\Phi}{A}$$

Therefore:

$$\Phi = AB$$

The flux around a coil of wire varies - &Lambda;NI only gives the total flux, not the flux across a certain area. To show this, we use lines of flux. These obey the following rules:

1. Lines of flux go from the north pole of a permanent magnet to the south pole.

2. Lines of flux go clockwise about wires carrying current away from you.

3. Lines of flux never touch, intersect, or cross.

The direction of the flux is shown with an arrow. Flux is a bit like electricity in that it must have a complete circuit. The lines of flux always take the route of most permeance. Iron (Fe) has around 800 times as much permeability as air. So, flux goes through the iron, and not the air.

Questions
1. A circular steel core has a cross-sectional area of 9 cm2, and a length of 0.5m. If the permeability of steel is 875 &mu;NA−2, what is the permeance of that core?

2. A coil of insulated wire is wrapped 60 times around the top of the core, and a 9A direct current is put through the coil. How much flux is induced?

3. Assuming that all the flux goes through the core, what is the flux density at any point in the core?

4. Draw a diagram showing the lines of flux within the core.

/Worked Solutions/