Physics › Magnetic fields › Magnetic flux and flux linkage
Magnetic flux and flux linkage
Before induction can be stated, it needs its own quantity. Flux counts the field threading an area; flux linkage multiplies by the turns of a coil; and one cosine, of the angle to the coil's normal, handles every tilt in between.
Builds on Magnetic flux density and the force on a wire.
IN THIS TOPIC
- Use Φ = BA for an area normal to the field, in webers.
- Use flux linkage NΦ, and NΦ = BANcosθ for a rotated coil, with θ to the normal.
- Describe the required-practical investigation with a search coil and oscilloscope.
WHAT YOU PROBABLY THINK
θ is the angle between the field and the coil.
Flux: field through an area
Picture the field as flow lines and ask how much passes through a chosen area. The magnetic flux through an area A held face-on to a field B, with B along the area's normal, is
measured in webers, where one weber is one tesla times one square metre. The name explains the other unit: flux density B is flux per unit area, webers per square metre, which is what a tesla is.
Linkage, and the tilt
A coil of N turns threads the same flux N times over, and the quantity that drives every result in electromagnetic induction is the flux linkage, NΦ. Tilt the coil and only the component of B along the coil's normal still counts:
where θ is the angle between B and the normal to the coil's plane, and that angle, misread, is the most reliable source of error in this topic. Face-on means θ = 0 and full linkage; edge-on means θ = 90° and none, even though the coil's plane then lies along the field. Check any answer against those two limits before trusting it.
Required practical 11: the search coil
The eleventh required practical measures how linkage depends on orientation with a search coil, a small many-turned coil on a handle, connected to an oscilloscope. Placed in an alternating field, the changing linkage induces an alternating pd whose amplitude on the screen is proportional to the flux linkage through the coil. Rotate the search coil in steps, read the amplitude at each angle, and a plot of amplitude against cosθ comes out straight: the cosine law confirmed by experiment, with the induction law it relies on arriving properly in the next lesson.
THE EXAM BIT
- Φ = BA needs B along the normal; for anything else, go straight to BANcosθ and say what θ is measured to.
- The limits are the self-check: θ = 0 (face-on) gives maximum linkage, θ = 90° (field in the coil's plane) gives zero. Quote them when explaining.
- Units earn marks: flux in webers, flux linkage in weber-turns, and one tesla is one weber per square metre.
- Read “rotated by” carefully: a coil rotated 30° from face-on has θ = 30°, but one rotated 30° from edge-on has θ = 60°. Draw the normal before substituting.
- In the practical, the oscilloscope's amplitude stands in for the linkage; plotting it against cosθ and getting a straight line through the origin is the analysis the mark scheme wants.
CHECK YOURSELF
A 500-turn coil of area 2.0 × 10−3 m² sits in a 0.15 T field with its normal at 60° to the field. Find the flux linkage, and state what it becomes face-on.
Show a hint
BANcosθ, with θ to the normal; then set θ to zero.
Show the answer
NΦ = BANcos θ = 0.15 × 2.0 × 10−3 × 500 × cos 60° = 0.075 Wb turns.
Face-on, cosθ = 1, so the linkage doubles to 0.15 Wb turns.
Edge-on it would fall to zero: the two limits that catch any misread angle.
Flux is field through area; linkage multiplies by the turns.
The cosine's angle runs to the normal, never the coil face.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.