Magnetic Flux Density Flux and Flux Linkage Elliott

Magnetic Flux Density, Flux, and Flux Linkage Elliott

We have seen how B is called the magnetic field strength, or the flux density, and is measured in Tesla, T. The magnetic flux density can be thought of as the concentration of field lines. We can increase the force by increasing any of the terms within the equation: F = Bil If we coil up the wire, we increase its length within the magnetic field. Flux density B is a vector.

Solenoid If we look at the magnetic field of a solenoid, we know that it is like a bar magnet: We can see that the magnetic field strength is uniform within the solenoid. However the flux density becomes less at the ends, as the field lines get spread out.

Flux We need a term that tells us the number of field lines, and it is called the magnetic flux. It is given the physics code Φ (Phi) It has the units Weber (Wb), where: 1 Wb = 1 T m 2 (therefore 1 T = 1 Wb m-2)

Formal Definition The product between the magnetic flux density and the area when the field is at right angles to the area. Write this in an equation

Φ = BA Flux is a vector

Flux Linkage The flux linkage is the flux multiplied by the number of turns of wire. If each turn cuts (or links) flux Φ, the total flux linkage for N turns must be N Φ. We can also write this as NBA. In other words: Flux linkage at its greatest

Check Your Progress How much flux links a 200 turn coil of area 0. 1 m 2 when it is placed at 90 o to a magnetic field of strength 2. 5 x 10 -3 T?

Answer

Varying Flux Linkage • Now we turn the coil through an angle θ • We now have to change our formula to take the angle into account:

Where the flux linkage is the greatest, q = 0, hence cos q = 1. If the coil were parallel to the field, q = 90 o therefore cos q = 0. The flux linkage can be changed in two ways: • We can alter the strength of the magnetic field; • We can alter the area at 90 o to the magnetic field by moving the coil. • If we are turning the coil, the new flux linkage is given by NBA�sin q where q is the angle the area makes to the magnetic field. • When we move a coil across a magnetic field, the area swept is the change in area (just like the change in distance is the distance moved).

Check Your Progress The coil in Question 1 is now turned so that it makes an angle of 60 o with the magnetic field lines. What is the change in flux linkage? (flux links a 200 turn coil of area 0. 1 m 2 when it is placed at 90 o to a magnetic field of strength 2. 5 ´ 10 -3 T)

Answer