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Question

# Figure shows a cross section of a large metal sheet carrying an electric current along its surface as shown in the figure. The current in a strip of width dl is kdl, where k is a constant. The magnetic field at a point P distance y from the metal sheet will be

A
μ0k
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B
μ0k2
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C
μ0k4
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D
32μ0k
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Solution

## The correct option is B μ0k2Consider two strips A and C of the sheet situated symmetrically on the two sides of P. Using right hand thumb rule, the magnetic field at P due to strips A and C will be equal in magnitude due to symmetry (say B). The resultant magnetic field B′ will be parallel to the sheet pointing leftwards as shown in the figure. The net field on the opposite side of sheet at the same distance will also be B′ but in opposite direction. Let us construct a rectangular ampieran loop as shown below, The net magnetic field on segment ad and bc will be zero. Using, Ampere's circutal law for loop: ∮→B.→dl=μ0Ien ⇒(B′l)+(B′l)=μ0(k)l or, 2B′l=μ0kl Why this Question? Note: The magnetic field due to current carrying infinite sheet is independent of the distance of the point from the sheet.

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