How Is the Magnetic Field Calculated at Point P Near a Current-Carrying Wire?

[amb0027]

Studying for a test, and can't figure out what the real answer is for this problem.

Homework Statement

There is a long vertical straight wire carrying a current Io upward. Use ampere's law to determine an expression for the magnetic field at point "P" a distance x from the long straight current carrying wire.

Homework Equations

Ampere's law: B =$$\mu$$_oI_o / 2$$\pi$$r

The Attempt at a Solution

B_p = $$\mu$$_oI_o / 2$$\pi$$x

Obviously not the right answer but I do not understand this stuff at all. Please explain? Thank you very much

 

[kuruman]

Ampere's Law is not what you say it is.

Go to

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html

Read what Ampere's Law is, understand it, then click the link "Magnetic field from a long straight wire". Read and understand that. These links provide as good an explanation as any that you can get on the web.

 

[amb0027]

I don't see the link "Magnetic field from a long straight wire" And i know what ampere's law is i just thought it broke down in this problem to what I stated. Trust me I've read plenty I just don't understand how to do this problem...

 

[AlexChandler]

To me it seems that your answer is correct.

Near a very long wire, if you imagine a circular loop of radius x whose area is perpendicular to the wire, we should have

$$\oint_C \vec B \cdot d \vec l = \mu_0 I_{enc}$$

Symmetry arguments tell us that the magnitude of the B field should be the same at all points on the loop, and the dot product should always give B dl. So we can pull the B out of the integral

$$B \oint dl = B * (2 \pi x) = \mu_0 I_{enc}$$

Which is the same answer you have.

What makes you think that this answer is wrong?

 

[amb0027]

Head of Physics Department at Auburn says its wrong haha.. but didn't give me the right answer, just marked through it.. he did give me one point, out of 10..

 

[AlexChandler]

Head of Physics Department at Auburn says its wrong haha.. but didn't give me the right answer, just marked through it.. he did give me one point, out of 10..

Perhaps you were marked down because you didn't actually use ampere's law.. you just used a special case formula derived from ampere's law.. I believe the answer is correct.

Maybe you should ask the professor who graded it why he marked it wrong.