# Development of Magentic force equation to include angle

1. Apr 3, 2012

### Da Apprentice

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

2. Apr 4, 2012

### Staff: Mentor

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?