# Magnetic field strength

## 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

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berkeman
Mentor

## 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?

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
Mentor
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... ?

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