Question

Two long wires a and b, carrying equal currents of 10.0 A, are placed parallel to each other with a separation of 4.00 cm between them as shown in figure. Find the magnetic field B at each of the points P, Q and R.

Answer 1

Net field at a point will be the vector sum of the fields due to the two wires. 

The magnetic field at P due to the wire a has magnitude

Its direction will be perpendicular to the line shown and will point downward in the figure. The field at this point due to the other wire has magnitude

Its direction will be the same as that of B₁.Thus, the resultant field will be 1.33 x 10^-4 T  also along the same direction.

Similarly, the resultant magnetic field at R will be 1.33 x 10^-4 T along the direction pointing upward in the figure.

The magnetic field at point Q due to the two wires will have equal magnitudes but opposite directions and hence the resultant field will be zero.