# Calculating EMF from Coils in Rotating Magnetic Field

• Lonley_Shepherd
In summary, the conversation discusses the calculation of the emf generated by two ten turn coils in a radial magnetic field. The first term of the equation is found to be zero due to the direction of A(phi) and B being at right angles. To account for this, a different area is chosen that encloses the same path, resulting in the same integral value. This accounts for the non-zero flux in the loop. However, choosing a larger area does not increase the magnitude value of the integral.
Lonley_Shepherd
To find the emf generated by two ten turn coils, the planes of which are at 60 degrees in a radial magnetic field B=Bcos(theta)sin(omega*t) in the direction Ar, that rotates with omega rad/sec at the instant when the coil A1A2 makes an angle alpha with the plane of the maximum flux density.

Now to compute the emf we will ignore the effect of mutual inductance and will just calculate the field for each coil then add them.

we have: emf = -N (integral) dB/dt . ds + N (integral) v x B . dL

my problem is with the first term, the S area vector is in the direction of A(phi) as shown (talking about the A1A2 coil here) so the dot product result will be zero even though the differential of B is not zero.

now i checked it with my tutor then he says we have to consider another area as the flux is clearly not zero (not that clear to me), so:
ds= r*d(phi)*dz Ar to get a value for the flux in the loop.. !

what i can manage so far that he chose another area that enclosed the same path, but isn't the value of that term going to increase if we choose larger areas, so the more the area "chosen" the more the flux!.. then there's no exact magnitude for any area integral .. thanks for your help

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Moved to homework forum.

Why is A(phi) dot B zero? In your figure, they are not at right angles to each other.

the three coordinate directions am using are: A(r) A(phi) and A(z)
isnt A(r) . anything but A(r) zero?? as in A(x) . A(y) is zero

PS: i am not really asking about that particular question its the concept of intergrating over a surface that encloses a path, as explained in the previous post.

thank you

Last edited:
Lonley Sheperd said:
what i can manage so far that he chose another area that enclosed the same path, but isn't the value of that term going to increase if we choose larger areas, so the more the area "chosen" the more the flux!.. then there's no exact magnitude for any area integral
It won't include a larger value of B dot dS. If the area is bounded by the same path, then the integral of the dot product should be the same. Like if the surface is a flat disk or a hemisphere, if the equator is the bounding path for each, then the integral of the dot product should be the same.

okay.. can u give me a numerical example for that..
if B= B(t) A(r) then it will move out of the integral sign and the only term remaining is the (integral) ds , so the more the area chosen the higher the magnitude value of that term.. please help me with that

## 1. How do you calculate the EMF in a rotating magnetic field?

To calculate the EMF (electromotive force) in a rotating magnetic field, you can use the formula EMF = B x L x v, where B is the magnetic field strength, L is the length of the coil, and v is the velocity of the rotation.

## 2. What is a rotating magnetic field?

A rotating magnetic field is a magnetic field that changes direction and magnitude as it rotates around a central point. It is commonly created by the interaction between multiple magnetic fields, such as those produced by different coils in an electric motor.

## 3. How does a rotating magnetic field generate electricity?

When a conductor, such as a coil, is placed in a rotating magnetic field, the changing magnetic field induces an electric current in the conductor. This is known as electromagnetic induction and is the basis for creating electricity in generators and motors.

## 4. What factors affect the EMF generated by a rotating magnetic field?

The EMF generated by a rotating magnetic field is affected by the strength of the magnetic field, the speed of rotation, and the length and orientation of the coil. Additionally, the materials used in the construction of the coil and the presence of any external magnetic fields can also impact the EMF.

## 5. How is the EMF in a rotating magnetic field used in practical applications?

The EMF generated by a rotating magnetic field is used in a variety of practical applications, such as in electric motors, generators, and transformers. It is also used in devices like induction cooktops and wireless charging pads.

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