Two parallel wires in plane. determine B field as f(x)

[cleverfield]

Homework Statement

Let two long parallel wires, a distance d apart, carry equal currents I in the same direction. One wire is a x=0 and the other is a x=d. Determine B along the x-axis between the wires as a function of X.

Repeat problem if wire at x=0 is 2I and in the opposed direction.

Homework Equations

Answer key = u/2pi * I [(d-2x)/(x(d-x))]

The Attempt at a Solution

I understand the physics, but I am unsure how to arrive at that final answer. I do not understand determining the point along the x-axis with those variables. Can someone please help me with the deriving?

 

[berkeman]

Homework Statement

Let two long parallel wires, a distance d apart, carry equal currents I in the same direction. One wire is a x=0 and the other is a x=d. Determine B along the x-axis between the wires as a function of X.

Repeat problem if wire at x=0 is 2I and in the opposed direction.

Homework Equations

Answer key = u/2pi * I [(d-2x)/(x(d-x))]

The Attempt at a Solution

I understand the physics, but I am unsure how to arrive at that final answer. I do not understand determining the point along the x-axis with those variables. Can someone please help me with the deriving?

Start with Ampere's Law, and do the vector addition. You are familiar with Ampere's Law and the Right-Hand Rule, right?

http://en.wikipedia.org/wiki/Ampère's_law

.

 

[cleverfield]

thanks for the reply. I know Amperes and vector, and maybe I'm not thinking this through properly. I know the direction of the magnetic fields. But how do you come up with a formula that is based on a variable "x" that could be any distance between the two currents?

 

[berkeman]

thanks for the reply. I know Amperes and vector, and maybe I'm not thinking this through properly. I know the direction of the magnetic fields. But how do you come up with a formula that is based on a variable "x" that could be any distance between the two currents?

Write the expression for the B-field for a single wire, as a function of the distance away from the wire (and with a vector direction from the RH Rule). Then stick the 2nd wire in there, and combine the two equations. With 2 wires and the currents going the same way, is the B-field halfway between them zero or twice what each wire makes on its own?

 

[cleverfield]

I know the expression is B=u/2pi * I/r ----- It is r that I have the problem with. How do you know r when it can vary from between 0 and d. where d is the max.

 

[berkeman]

I know the expression is B=u/2pi * I/r ----- It is r that I have the problem with. How do you know r when it can vary from between 0 and d. where d is the max.

Exclude r=0 because of the infinity it introduces. For all r>0, the solution is straightforward, no?

 

[cleverfield]

Unfortunately no.

For the equation with just one wire i have:

B=u/2pi*I/xfor the second wire it would be

B=u/2pi*I/d-xEven if this is right, I am not sure where to go next.