# Two large metal sheets carry surface currents as shown in figure. The current through a strip of width dl is Kdl where K is a constant. Find the magnetic field at the points P, Q and R.

Ampere’s circuital law states that the line integral of the magnetic field for a closed surface is μ0 times the current enclosed by the surface.

, where B = magnetic field, dl = line element, μ0 = magnetic permeability of vacuum, I = current enclosed.

(i) At point P, the current enclosed(I) = 0.

Hence, from Ampere’s circuital law, B.dl = 0 => B (magnetic field at P) = 0. (Ans)

(ii) Point Q is in between the two strips carrying current.

Hence, from Ampere’s circuital law, we consider only B.dl for the strip of width dl carrying surface current K. Hence, I (current enclosed by the strip) = Kdl.

Therefore, B.dl = μ0Kdl => B (magnetic field at Q) = μ0K (Ans)

(iii) At point Q, again, current enclosed(I) = 0.

Hence, from Ampere’s circuital law, B.dl = 0 => B (magnetic field at Q) = 0. (Ans)

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