Magnetic field strength between two wires

[victoriafello]

wire 1 has a current of 1A directed into the page, wire 2 is 20 cm to the right of wire 1 with a current of 1A, what direction does this current have to flow in order for the magnetic field strength at the mid point between them to be non zero ?

from the right hand rule the mag field from wire 1 would be counterclockwise around the wire so the current on wire 2 would have to be the same direction - into the page with a counterclockwise field other wise the fields would cancel

do i haev this correct & did i explain myself properly ? the next part of the Question depends on this answer

 

[Spinnor]

The current into the page gives a clockwise field via the right hand rule, if I'm not mistaken. Draw a picture, I think you came up with the wrong conclusions.

 

[victoriafello]

thanks for pointing that out, i have drawn a picture of the wire and i can see now that the current is clockwise, so i think that the current in the other wise also needs to be into the page otehrwise they will cancel,


the next part of the question is -
Consider a general point on the line joining the two wires and a distance d away from the mid-point O. By summing the magnetic field due to currents of magnitude i flowing in both the wires in the senses you found.

show that, on the line joining the two wires, the magnetic field strength is given by
B= μo iD/ PI (D^2 − d^2 )

I know the equation is

B = μo i / 2*pi*d

and (D^2-d^2) can become (D+d)(D-d) but i don't know where to go from there

 

[Spinnor]

If currents are in the same direction the field will tend to cancel between the wires being zero at the midpoint. See:

http://ptsg.eecs.berkeley.edu/~helens/edu/sol_page/solenoid.gif

http://pagesperso-orange.fr/lempel/geomag/Boucle.gif

As for the second part try and write down the field at some specific point like say 1 meter to the right, distances measured with respect to the origin. If you do so I think you will see what you must do to get the answer.