Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O. The net magnetic field at O is:

Question

G1 Physics · Accepted Answer

Point O lies on the common axis and is at distance r from the centre of each circular loop. Magnetic field on the axis of a circular loop of radius r at axial distance x is B = μ₀Ir²/ [2(r²+x²)³ᐟ²]. Here, x = r. Therefore the field at O due to loop P is B(P) = μ₀Ir²/ [2(2r²)³ᐟ²] = μ₀I/(4√2r). Loop Q carries current 4I, so B(Q) = 4B(P). Because both currents are clockwise as seen from O but the loops lie on opposite sides of O, their magnetic fields at O are in opposite directions. The stronger…