Wrong B-Field Result: What Should I Have Done?

[rmrribeiro]

Homework Statement

I need to calculate de B (in a position along the axis) field created by a disk with current I.
The parametera were:
Radius of the disk: a=0,007 m
Current: I=1,07 A
Miu0= 1,2566E-6 NA-2
The position: Z=0,0593m

Relevant Equations

THe b filed along the a spire (or loop)
B= (Miu0 . I) (a^2/(a^2+z^2)^(3/2)

I integrated B within the limits of a (from 0 to 0.007)
teh result was 3.64E-10 T and it was wrong. the correcto one would be 5.8 E-4 T and it is a major diference (aprox 1 million times )
Waht shoud I have done?

Regards

 

[PhDeezNutz]

Is it possible that you put in the wrong form of $dA$ (differential area element) when integrating over the disk?

$dA = r dr d \theta$ for your double integral.

 

[vela]

Homework Statement:: I need to calculate de B (in a position along the axis) field created by a disk with current I.
The parametera were:
Radius of the disk: a=0,007 m
Current: I=1,07 A
Miu0= 1,2566E-6 NA-2
The position: Z=0,0593m
Relevant Equations:: THe b filed along the a spire (or loop)
B= (Miu0 . I) (a^2/(a^2+z^2)^(3/2)

I integrated B within the limits of a (from 0 to 0.007)
teh result was 3.64E-10 T and it was wrong. the correcto one would be 5.8 E-4 T and it is a major diference (aprox 1 million times )
Waht shoud I have done?

Please show your work so we can see what you actually did.

 

[rmrribeiro]

 

[rmrribeiro]

My approach was that a disk is a “infinite” number of circular loops with radius between the values of ‘a’

 

[vela]

Your approach is clearly wrong because it produces a result with the wrong units. You're multiplying an expression which has units of T with da which has units of m, so your answer is going to be T•m, not just T as you want.

What does it mean for a disk to carry a current $I$? It makes sense to talk about a current going around a ring. There's only one path the charges can follow, but that's not the case for a disk. Can you post the actual problem statement?

 

[rmrribeiro]

The B field in a loop with current I is guiven by (at a guiven distance along the axis)
B=(μ0 . I) (a^2/(a^2+z^2)^(3/2)

If we have a continuos set of rings from 0 to 0.007 m, each with a current I= 1.07 A, what would be the B field in a point at 0.0593 m along the axis?

 

[vela]

If each infinitesimal ring carried a finite current of 1.07 A, there would be an infinite current flowing around the center of the disk because you would need an infinite number of rings. The field at z would be infinite.

 

[rmrribeiro]

I realised that, but believed it to be some sort of missusing of words. ANd the suposed correct solution is B(0,0593)=5.8E-4 T

 

[vela]

Well, without a well-posed problem, you're just guessing.

In any case, the supposed answer seems to be unrealistically large given the numbers in the problem. If you calculate the field at $z$ for a ring of radius $a$ carrying current $I$, the field is many orders of magnitude smaller than the supposed answer to the problem. I don't see how spreading the current around on a disk is going to change that.

 

[haruspex]

I realised that, but believed it to be some sort of missusing of words. ANd the suposed correct solution is B(0,0593)=5.8E-4 T

My guess would be that the current is supposed to be uniformly distributed across the disc, so each ring element width dr carries a current $\frac {Idr}R$.