Induced EMF on a rotating coil

In summary, at the moment, the coil is rotating at a frequency of 1800 rpm and has a magnetic field of 0.365 tesla. The emf induced in the coil is 1.8V.
  • #1
B4ssHunter
178
4

Homework Statement



a coil starts perpendicular to a magnetic field of 0.365 tesla , it has a length of 0.15 cm and a height of 0.25 cm , it rotates with a frequency of 1800 rotation / min . it also has 30 turns
calculate the mean induced Emf during quarter a rotation

Homework Equations


emf = rate of change of magnetic flux / sec


The Attempt at a Solution


i have already solved the problem , during quarter a rotation , the magnetic field goes from 0.365 to 0 because in a quarter rotation , the coil goes from 90 degrees to 0 degrees with the field .
a quarter rotation takes a time of 1/30 /4 = 1/120 sec.
but i don't really want to find that , i want to use calculus to find the exact rate of change at a particular moment
now weber = area * field * sin theta
where theta is the angle between the coil and the field
now the rate of change of weber = area * field * cos theta * rate of change of theta .
when it takes a quarter of rotation , the theta will be 0 so cos theta = 1 , but how do i exactly find the rate of change of theta ?
if it takes 360 degrees / (1/30) seconds , is that the rate of change of theta ? , how do you exactly find dtheta / dt ?
 
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  • #2
θ=ωt
 
  • #3
B4ssHunter said:

Homework Statement



a coil starts perpendicular to a magnetic field of 0.365 tesla , it has a length of 0.15 cm and a height of 0.25 cm , it rotates with a frequency of 1800 rotation / min . it also has 30 turns
calculate the mean induced Emf during quarter a rotation

now weber = area * field * sin theta
where theta is the angle between the coil and the field

now the rate of change of weber = area * field * cos theta * rate of change of theta .


Not right. See below.

when it takes a quarter of rotation , the theta will be 0 so cos theta = 1 , but how do i exactly find the rate of change of theta ?
if it takes 360 degrees / (1/30) seconds , is that the rate of change of theta ? , how do you exactly find dtheta / dt ?

The way you described the orientation of the field, it's weber = area x field x cos(theta). So let's be scientific and say ψ = AB cosθ. I use ψ since phi never shows up in my toolbar. θ is the angle between the B field and the normal to the coil. You have to be precise when you say " ... a coil starts perpendicular to a magnetic field ... ". That could mean that two of the four sides of the coil are perpendicular to the field. Anyway, we start at θ = 0 and go to θ = π/4.

So, what is the emf induced in the coil at any moment? Hint: Faraday plus hint of post #2.

And, 1800 rotations per minute is how much dθ/dt?
 

1. What is Induced EMF on a rotating coil?

Induced EMF (electromotive force) on a rotating coil is a phenomenon where a changing magnetic field induces an electric current in a coil that is rotating within the field. This is also known as Faraday's law of induction.

2. How does Induced EMF on a rotating coil occur?

Induced EMF on a rotating coil occurs when there is a change in the magnetic field passing through the coil. This can happen when the coil rotates within a fixed magnetic field, causing the magnetic flux through the coil to change, which then induces an electric current in the coil.

3. What factors affect the magnitude of Induced EMF on a rotating coil?

The magnitude of Induced EMF on a rotating coil depends on the strength of the magnetic field, the speed of rotation of the coil, and the number of turns in the coil. A stronger magnetic field, faster rotation, and more turns in the coil will result in a higher induced EMF.

4. What is the relationship between the direction of rotation and Induced EMF on a rotating coil?

The direction of rotation of the coil plays a significant role in determining the direction of the induced EMF. According to Lenz's law, the induced EMF will always be in a direction that opposes the change in magnetic flux through the coil. This means that the direction of the induced current will be opposite to the direction of rotation of the coil.

5. What are the applications of Induced EMF on a rotating coil?

Induced EMF on a rotating coil has various real-world applications, including in electric motors, generators, and transformers. It is also used in devices such as magnetic tape recorders and induction cooktops. Understanding induced EMF is crucial in the development of many technologies and plays a significant role in the study of electromagnetism.

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