# Calculating Flux Linkage in a Rotating Rectangular Coil

• MemoNick
In summary, the problem involves a flat rectangular coil measuring 2cm x 3cm with 60 turns of wire, rotated through 90 degrees in 0.2s. The flux density of the magnetic field is 0.30T. To find the change of flux linkage, the formula Φ = BAN is used, where B is the magnetic field, A is the area of the coil, and N is the number of turns of wire. The initial flux linkage is maximum and the final is minimum (0), so the equation becomes Φ = BA(initial) - BA(final). After calculation, the resulting flux linkage is 1.8 x 10-4Wb. It is important to include units and
MemoNick
1. A flat rectangular coil measuring 2cm x 3cm and having 60 tuns of wire is turned through 90 degrees in 0.2s. The flux density of the magnetic field is 0.30T. Please note that a diagram is also provided - basically the coil is first perpendicular to the field, then it's rotated so as to become parallel. (Note that there are two parts for this question - the part I'm having problem with requires to find the change of flux linkage)
I don't know which formula/e I should have used, although given the dimensions, I guessed I would have to use $\vartheta$ = BA
3. Since at first, the flux linkage is maximum, and when rotated the linkage is minimum (0), I was tempted to use $\vartheta$ = BA [initial] - BA [final, where B = 0]
Therefore: $\vartheta$ = 0.3 * 0.02 * 0.03 = 1.8 x 10-4Wb
Now, my question is - is my reasoning correct? Thanks in advance!

Last edited by a moderator:
Welcome to PF!

Basically, you have the right reasoning. But the definition of flux linkage includes the number of turns of wire.

You might also need to consider the sign of the answer to indicate whether there was an increase or decrease in flux linkage.

1 person

Yeah, sorry - I forgot the units. What should I do with the number of turns of the wire?

## 1. What is flux linkage?

Flux linkage is a measure of the amount of magnetic flux that passes through a circuit or coil. It is the product of the number of turns in the coil and the magnetic flux passing through each turn.

## 2. How is flux linkage calculated?

Flux linkage is calculated by multiplying the number of turns in a coil by the magnetic flux passing through each turn. This can be represented mathematically as Φ = NΦm, where Φ is the flux linkage, N is the number of turns, and Φm is the magnetic flux.

## 3. What is the unit of measurement for flux linkage?

The unit of measurement for flux linkage is weber-turns (Wb-turns) or volt-seconds (Vs). This unit is derived from the product of webers (Wb), the unit of magnetic flux, and turns, the unit of measurement for the number of turns in a coil.

## 4. How does flux linkage relate to electromagnetic induction?

Flux linkage is a key concept in understanding electromagnetic induction. When a coil is exposed to a changing magnetic field, the flux linkage also changes, inducing an electromotive force (EMF) in the coil. This is the basis for generating electricity in devices such as generators.

## 5. What factors affect the calculation of flux linkage?

The calculation of flux linkage is affected by the number of turns in the coil, the strength of the magnetic field, and the orientation of the coil in relation to the magnetic field. Other factors that can influence flux linkage include the material of the coil and the magnetic permeability of the surrounding medium.

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