# Why Does the Trigonometric Function in the FEM Calculation Differ?

• LCSphysicist
In summary, the conversation discusses finding the FEM induced in a rotating coil inside a solenoid. The formula provided is $$\phi = \langle B,A \rangle = \mu n I \pi r^2 N cos(\theta = wt)$$ with the variables ##r##, ##n##, ##N##, ##w##, and ##I##. The disagreement between the two answers may be due to a difference in definitions for the variable ##\theta##. The importance of knowing the solenoid's axis of symmetry is also mentioned.
LCSphysicist
Homework Statement
..
Relevant Equations
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I need to find the FEM induced in a coil that rotates around the y-axis and is inside a solenoid. The coil starts in the plane yz
##r## is the radius of the coil
##n## is the number of spiral by length of the solenoid.
##N## is the number of turns of the coil
##w## is the angular velocity that the coils rotate.
##I## is the current passing through the solenoid

I just thought this:
$$\phi = \langle B,A \rangle = \mu n I \pi r^2 N cos(\theta = wt)$$
$$\epsilon = -\dot \phi = \mu n I \pi r^2 N w sin(\theta = wt)$$

This is a simple exercise. But i can't see why my answer is wrong. That is, the answer provided by the list is ## \mu n I \pi r^2 N w cos(\theta = wt)##. The trignometric function is different. My answer says that at t=0 the induced FEM is zero, the other says it is maximum.

Sorry, what's FEM?

Delta2
Which axis is given as the solenoid’s symmetry axis? This is a vital piece of information. This is why you are asked to provide the homework statement verbatim, which you have ignored.
berkeman said:
Sorry, what's FEM?
Based on context, I would assume the OP is not a native English speaker and the original language is a Latin language. FEM would really be EMF, electromotive force.

Delta2, rsk and berkeman
Herculi said:
My answer says that at t=0 the induced FEM is zero, the other says it is maximum.
Is your definition of variable ##\theta## the same as the definition in the "other"? If yours differs by 90o from the "other", then that could be the source of the disagreement.

Delta2

## 1. What is FEM induced in a coil?

FEM (Faraday's Law of Electromagnetic Induction) induced in a coil is the process by which a changing magnetic field creates an electric current in a nearby coil. This is based on the principle that a changing magnetic field induces an electric field, which in turn causes a current to flow in a conductor, such as a coil.

## 2. How is FEM induced in a coil?

FEM induced in a coil occurs when there is relative motion between a magnet and a coil, or when the magnetic field strength changes over time. This can be achieved by moving a magnet towards or away from a coil, or by changing the current in a nearby coil. The changing magnetic field induces an electric field, which causes a current to flow in the coil.

## 3. What are the applications of FEM induced in a coil?

FEM induced in a coil has a wide range of applications, including power generation, electric motors, transformers, and wireless charging. It is also used in devices such as generators, microphones, and speakers.

## 4. How is FEM induced in a coil related to electromagnetic waves?

FEM induced in a coil is closely related to electromagnetic waves, as both involve the interaction between electric and magnetic fields. Electromagnetic waves are produced when an electric field oscillates, which in turn creates a changing magnetic field. This changing magnetic field can then induce an electric current in a nearby coil, resulting in FEM induction.

## 5. What factors affect the strength of FEM induced in a coil?

The strength of FEM induced in a coil depends on several factors, including the strength of the magnetic field, the number of turns in the coil, the speed of the relative motion between the magnet and coil, and the resistance of the coil. Additionally, the material and size of the coil can also affect the strength of FEM induced in a coil.

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