Magnetic Field Strength at a Point Along an Infinite Wire

[frostking]

Homework Statement

A current I flows to the right on the x-axis from the origin to x = infinity. What's the magnitude of the magnetic field at (x,y) = (0,L)?

Homework Equations

B = u sub 0 time I/(2 pi R)

The Attempt at a Solution

We use above equation since we have an extremely long wire. I would think I should just replace the R for the L as the given point value of y. However, this is an old exam question and the professor's solution states that B ' = 1/2 B and therefore the answer is:

u sub 0 times I / (4pi L) Could someone please explain why the statement of B' = 1/2 B makes sense. If I know that then of course the answer in the exam key would make perfect sense! Thanks for your time and effort, Frostking

 

[berkeman]

Homework Statement

A current I flows to the right on the x-axis from the origin to x = infinity. What's the magnitude of the magnetic field at (x,y) = (0,L)?

Homework Equations

B = u sub 0 time I/(2 pi R)

The Attempt at a Solution

We use above equation since we have an extremely long wire. I would think I should just replace the R for the L as the given point value of y. However, this is an old exam question and the professor's solution states that B ' = 1/2 B and therefore the answer is:

u sub 0 times I / (4pi L) Could someone please explain why the statement of B' = 1/2 B makes sense. If I know that then of course the answer in the exam key would make perfect sense! Thanks for your time and effort, Frostking

The only thing I can think of is the strange statement that the current flows "right on the x-axis from the origin to x = infinity". How does the current return from infinity to the origin? It can't just magically appear at the origin and flow away. Is there a diagram associated with the problem?

 

[frostking]

There is no diagram and no explanation of this magical B' that he comes up with. The only thing I can figure is that the wire goes from negative infinity to positive infinity and therefore we are only considering 1/2 of the total. What do you think of that? Thanks for your time! Frostking

 

[berkeman]

There is no diagram and no explanation of this magical B' that he comes up with. The only thing I can figure is that the wire goes from negative infinity to positive infinity and therefore we are only considering 1/2 of the total. What do you think of that? Thanks for your time! Frostking

Yeah, that seems to be what is being asked, but the non-physical nature of the question is problematic. Maybe try different ways of routing the current back to the origin, to see if you can cancel out the x-component of the B-field that would result from only counting the current from the origin to infinity... ?

 

[frostking]

Thanks for your input. I hope the test tomorrow night has more concrete questions! Frostking