Development of Magentic force equation to include angle

In summary: There doesn't seem to be a mention of force in the conversation, only the number of coils and the magnetic field. In summary, the conversation is discussing the adaptation of a formula to include the angle made by the coils relative to the cylindrical core of an electromagnet. The equation for determining the number of coils is given, taking into account the length of the wire, the angle, and the circumference of the cylinder. The formula for determining the magnetic field is also adjusted to include the angle. However, there is no mention of force in the conversation.
  • #1
Da Apprentice
59
0
Hi All,

B = μonI
I am trying to adapt this formula to include a dependence upon the angle made by the coils relative to the cylindrical core of the electromagnet. For example it is known that the number of coils (n) that can be formed around a cylinder should be dependent upon the length of the given wire (l), the angle made between the wire and the cylinder (θ) and the circumference of the cylinder (2(pi)r). Where the number of coils should be proportional to length, inversely proportional to the circumference and proportional to the sine of the angle)

Therefore the equation used to determine the number of coils should be;

n = k(sin(θ)*l)/(2(pi)r)
Where k is some constant, With the assumption made that the wire is wound as tightly to the cylinder as possible (there isn't a gap between the wire and the cylinder).

Therefore the main equation can be written as;

B = k(μoI(sin(θ)*l))/(2(pi)r)
Is this a correct equation for determining the force based upon the angle made by the coils relative to the cylindrical core or is there another variable which I am overlooking?

Thanks,
Z.C
 
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  • #2
If I understand your setup correctly, you get a low density of windings (if sin(theta) is not close to 1). In that case, the formula B=my_0 n I might be a bad approximation.

>> Is this a correct equation for determining the force
Force?
 

1. How is the magnetic force equation derived?

The magnetic force equation is derived from the Lorentz force law, which states that the force on a charged particle moving in an electric and magnetic field is given by the cross product of the electric field and the particle's velocity, and the dot product of the magnetic field and the particle's velocity.

2. Why is the angle between the magnetic field and the velocity important in the magnetic force equation?

The angle between the magnetic field and the velocity is important because it affects the magnitude and direction of the magnetic force. The greater the angle, the smaller the magnitude of the force and the more it deviates from the direction of the magnetic field.

3. How is the angle included in the magnetic force equation?

The angle is included in the magnetic force equation through the use of trigonometric functions, specifically the sine and cosine functions. The angle is used to determine the component of the velocity that is parallel and perpendicular to the magnetic field, which in turn affects the magnitude and direction of the force.

4. Can the magnetic force equation be used for any angle between the magnetic field and the velocity?

Yes, the magnetic force equation can be used for any angle between the magnetic field and the velocity. However, it is most commonly used for angles between 0 and 90 degrees, as these are the most common angles encountered in real-world applications.

5. How does the inclusion of the angle in the magnetic force equation impact its applications?

The inclusion of the angle in the magnetic force equation allows for more accurate calculations and predictions of the behavior of charged particles in magnetic fields. It also allows for the optimization and control of magnetic systems, such as in particle accelerators and MRI machines.

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