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Figure shows a cross section of a large ...

Figure shows a cross section of a large metal. Sheet carrying an electric current along its surface. The current in a strip of width dl is Kdl where K is a constant. Find the magnetic field at a point P at a distance x from the metal sheet.

Text Solution

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Solution: Consider two strips A and C of the sheet
situated symmetrically on the two sides of P.
The magnetic field at P due to the strip A is
`B^a perpendicular of AP and that due to the strip C is
B^c perpendicular to CP. The resultant of these two is
parallel to the width AC of the sheet. The field due to
the whole sheet will also be in this direction. Suppose
this field has magnitude B.
` The field on the opposite side of the sheet at the same`
distance will also be B but in opposite direction. Applying
Ampere's law to the rectangle shown in figure.
` 2Bl= (mu_0)Kl`
`or, B= 1/2(mu_0)K.`
Note that it is independent of x.
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