Shown at right is a cross-sectional view of two long straight wires that are parallel to one another. One wire carries a current out of the page; the other carries an equal current into the page. I don't know how to show the diagrams, but the current into the page is at (3,0), the current out of the page is at (8,5) and P is at (8,0). I'm judging this by their locations in the diagram.
a. Draw a vector on the diagram to show the direction of the magnetic field, if any, at point P. Explain your reasoning.
b. Suppose that a third wire, carrying another current out of the page, passes through point P. Draw a vector on the diagram to indicate the magnetic force, if any, exerted on the current in the new wire at P. If the magnitude of the force is zero, indicate that explicitly. Explain your reasoning.
c.Suppose instead that the third wire (carrying the same current out of the page) is placed such that the magnetic field at point P has zero magnitude. Determine the location of the third wire. Clearly indicate on the diagram at right the correct location of the new wire. Explain how you determined your answer.
The Attempt at a Solution
a. I drew the vector at point P 45 degrees southeast because the B-field from the wire with the current into the page is flowing clockwise, while the B-field from the wire with the current out of the page is flowing counter-clockwise. By using the right hand rule, the fields are pointing right and down at P respectively. When I add the two vectors, the resultant vector is 45 degrees to the bottom-right.
b. For this, I used F = I x B and the right hand rule. I is out of the page at P and the direction of B is the same as in part a. By doing the cross-product, I said that the force must point upward.
c. I have no idea how to do this part. If anyone can explain how I'm supposed to go about this, I really appreciate it!
Also, if anyone can verify my answers for the parts a) and b), that would be great!