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The question: Two crisscrossing insulated wires contain currents as displayed. Find the total mag field at points P and Q, assuming the horiz current moves (a) right and (b) left. QUESTION is for part a.

I assumed going out of the page = + and going into the page = - (since it doesn't matter). The answer says that at point P, the field caused by the 12A current wire is into the page, while at point Q, the field is going out of the page.

I am having trouble understanding this. I know the RH rule for figuring out the direction of the field (thumb in direction of I, fingers curl in direction of B), but I have trouble applying it to points. I don't understand what the difference is at point Q and point P for the directions. It would be great if someone can clearly clarify for me, preferably using the RH rule!

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An easy way to find the direction is to use the cross product method.Direction of magnetic field by any small element dl can be found out by Cross product of direction of current and displacement vector r from that element. Consider a small element dl parallel to p on 12 ampere wire.direction of current is towards y axis,direction of displacement vector r is towards X axis.Now cross product of a vector in y direction with a vector in X direction gives a vector in minus z direction i.e into plane of paper.Similarly,you can see that due to each element of wire of 12 A it will be into plane of paper.

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First, recall that the field goes like $1/d$ with $d$ the distance from the wire. Using the RHR, the field for the vertical wire will be into the page at P (your finger curl into the page at that point) and out of the page at Q (your finger curl out the page a that point).

Now for the horizontal wire. In case b) the field is out of page at P and into the page at Q, again using RHR. Now add this to the field of the vertical wire. The field strength of the horizontal one wins in both cases because P and Q are closer to the horizontal than the vertical wire. Thus, the net field in this case is into the page at P and out of the page at Q.

Case a) done in a similar way.

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