How Does the Biot-Savart Law Apply to Two Perpendicular Current-Carrying Wires?

[andrew410]

Two very long, straight, parallel wires carry currents that are directed perpendicular to the page, as in the figure below. Wire 1 carries a current I1 into the page (in the -z direction) and passes through the x-axis at x=+a. Wire 2 passes through the x-axis at x=-2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude (2*permeability of free space)/(2*pi*a) The current I2 can have either of two possible values.

I know how to get the magnetic field at a point P for one current carrying wire, but I don't understand how to get the magnetic field at a point P for two current carrying wires. I know that the magnetic field at a point P for one current carrying wire is B=(permeability of free space * I)/(2*pi*a).

I need some help...Any help would be great. Thx in advance!

 

[dextercioby]

HINT:Add them as vectors...Meaning the two distinct contributions from each current/wire...

Daniel.

P.S.It's not Biot-Savart(-Laplace) law here...It's more like Ampère...

 

[logicalman]

Two very long, straight, parallel wires carry currents that are directed perpendicular to the page, as in the figure below. Wire 1 carries a current I1 into the page (in the -z direction) and passes through the x-axis at x=+a. Wire 2 passes through the x-axis at x=-2a and carries an unknown current I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude (2*permeability of free space)/(2*pi*a) The current I2 can have either of two possible values.

I know how to get the magnetic field at a point P for one current carrying wire, but I don't understand how to get the magnetic field at a point P for two current carrying wires. I know that the magnetic field at a point P for one current carrying wire is B=(permeability of free space * I)/(2*pi*a).

I need some help...Any help would be great. Thx in advance!

Point your "thumb" in the direction of the flow of current and curl your four fingers around the wire (just like when you jack off), the direction of your four fingers is the direction of the magnetic field, do the same for the other 2nd wire. If one time your fingers point clockwise and other time anticlockwise then subtract the magnetic field othewise add.

 

[dextercioby]

Point your "thumb" in the direction of the flow of current and curl your five fingers around the wire (just like when you jack off), the direction of your five fingers is the direction of the magnetic field, do the same for the other 2nd wire. If one time your fingers point clockwise and other time anticlockwise then subtract the magnetic field othewise add.

Does that mean that u assumed he/she has 6 fingers at one hand (at least)...

Daniel.