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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 μ0k2
Consider 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

(Bl)+(Bl)=μ0(k)l

or, 2Bl=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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