Two identical circular loops, P and Q, each of radius r and carrying currents I and 2I respectively are lying in parallel planes such that they have a common axis. The direction of currents in both the loops is clockwise as seen from O which is equidistant from both the loops. Find the magnitude of the net magnetic field at point O.

Dear Student,
  We have magnetic field due to circular loop of radius r at its axis at distnce a B=μ0ir22(a2+r2)3/2So in this caseB=μ0Ir22r2+2r223/2 =μ0I25/2rNow, current is flowing in loop P in clockwise directionSo by using right hand thumb's rule the direction of magnetic field will be towards leftBP =μ0I25/2r  Pointing towards PSimilarly for loop Q current is in clockwise direction so magnetic field due to it in leftBQ =μ0I25/2r  Pointing towards PSo magnetic field due to both loop will be in left direction means in same direction so net magnetic field =sum of both magneic fieldBnet =2μ0I25/2r=μ0i23/2r
Regard

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