Solve "Wires and Currents" Homework w/ Answers

[candyq27]

Homework Statement

Two very long straight wires carry currents perpendicular to the page. Wire 1, which carries a current I1 into the page, passes through the x-axis at x=+a. Wire 2, located at x=-2a, carries an unknown current.
The net field at the origin (x=0), due to the current-carrying wires has a magnitude of B= (2*uo*I1)/(2*pi*a)
a) What is the magnitude and direction of the current in wire 2? Find all possible solutions.
b) For your solution to part (a) for which I2 has the largest magnitude, determine the location of all points on the x-axis, a finite distance from the wires, at which the net magnetic field is zero.

Homework Equations

B=(2*uo*I1)/(2*pi*a)
V=IR
I=Q/t
?

The Attempt at a Solution

I'm really not sure how to go about doing this problem. I started by doing (uo*I)/(2*pi*a) + B = (2*uo*I1)/(2*pi*a) but then I really don't know where I"m going with it. Please help me work through this. Thanks!

 

[robb_]

Remember that B is a vector field. Can you draw the B field at the origin due to the individual fields, (this requires knowledge of what the field depends upon and use of a right hand rule if you will), and then the total field?

 

[candyq27]

At the origin, using the right hand rule knowing that at point a it is pointing into the page, the B would be going to the right I think..?

 

[robb_]

No. Point your right thumb in the direction of the current (conventional) and your fingers will curl in the direction of the field.

 

[candyq27]

That's what I did. My thumb points into the page so my fingers curl to the right

 

[robb_]

Now wait, rotate the picture so that your thumb still points in the direction of the current. WHat does this tell you about the field?
As for the second wire, the current, in general, can point into or out of the page. Why not see if both are possible?

 

[candyq27]

Now wait, rotate the picture so that your thumb still points in the direction of the current. WHat does this tell you about the field?
As for the second wire, the current, in general, can point into or out of the page. Why not see if both are possible?

I'm not sure what the first part means. If i rotate the picture then it can be anywhere.
If the current points into the page the field is going to the right and if it points out of the page the field is going to the left. I don't understand how to tell which direction is the correct direction for the point though.

 

[robb_]

I am not sure you are picturing the B field from a long current carrying wire correctly.
You used the RHR and saw that your fingers curled to the right, because of the orientation of your hand/arm. If you take your piece of paper with the current drawn into the page and rotate it by 180 and use the RHR again, what do you find? Both answers are correct, if you are using the RHR correctly.

 

[candyq27]

I grab the wire and point my thumb out and the direction of my fingers is the direction of the field, so it is either to the right or to the left depending on which way I turn my thumb.

 

[robb_]

Maybe you should consult your text for the field around a long current carrying wire. You should have a conceptual picture to think about before you calculate.