Question

Equal amount of current is flowing in two insulated wires perpendicular to each other as shown. Which segment A, B, C or D has the strongest magnetic field flowing out of the paper?

Answer 1

Hint: Firstly, you could recall which rule will give us the direction of the magnetic field produced by a current carrying conductor. Then you could separately apply this rule to each of the given wires and then combine. Lastly, you could find where the magnetic field due to both wires is directed outward and that will be our answer.

Complete answer:
In the given question, we are given two insulated wires that are kept perpendicular to each other. This arrangement divides the region into four parts, namely, A, B, C and D. We are asked to find the segment that has the strongest magnetic field directed outward.
In order to answer this question, all we have to do is to find the direction of the magnetic field due to each insulated wire in each of the given regions.
We know that the direction of the magnetic field due to long current carrying wire can be given by right hand thumb rule. You could curl your right hand around the wire in a way that the thumb points in the direction of the current in the wire, then, the direction of the curl of the rest of the fingers will give us the direction of the magnetic field.
Let us consider each wire separately.

Here, the cross indicates that the magnetic field is directed inward and the dot represents the magnetic field directed outward. Now for the other wire,

Combining the two we get,

So, in region A, we have fields due to both wires directed outwards, in region B and D we have fields due to one wire directed inward and due to other wires directed outward, and in region C we have fields due to both wires directed inwards. Hence, we found that it is region $A$ that has the strongest magnetic field flowing out of the paper.

Note: Let us discuss some characteristics of magnetic fields produced by a current carrying conductor. This field is found to encircle the conductor lying in a plane perpendicular to the conductor. The magnetic field strength is found to be directly proportional to the current magnitude and inversely proportional to the distance of the point from the wire where the field strength is to be found.