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Calculate the ratio of magnetic field at...

Calculate the ratio of magnetic field at a point ` (a)/(2)` above the surface of the wire to that at a point `(a)/(2)` below its surface. What is the maximum value of the field of this wire?

Text Solution

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Magnetic field at a point a/2 above the surface of the wire
`B_(out ) = (mu_(0)I)/(2 pi r) = (mu_(0)I)/(2pi (a//2))`
`= (mu_(0)I)/(pi a)`
Magnetic field at a point a /2 below its surface ,
`B_(n ) = (mu_(0)I)/(2 pi ) . (r )/(a^(2))`
`= (mu_(0)I)/(2pi) . (a//2)/(a^(2))`
`= (mu_(0)I)/(4pi a)`
`:. (B_(out))/(B_(n))= (mu_(0)I//pi a)/(mu_(0)I // 4 pi a)`
` (B_(out))/(B_(n))= (4)/(1)`
Maximum value of the field in the wire
`= (mu_(0)I)/(2 pi a ) ` ( at the surface)
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