Q.

We want to find the magnetic field B due to an infinite slab of current, using Ampere's law. The figure shows a slab of current with current density J=Jz^, where dimensions of j are amps per square meter.  The slab of current is infinite in the x and z directions, and has thickness d in the y-direction.

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Magnetic field at y<d/2 is  nμ0jy. The value of n is….

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Detailed Solution

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Consider a strip of length h  along x-axis and thickness dy along y-axis.
Current through the strip,
I=area   of  stripcurrent  density=hdyj

Apply Ampere’s circuital law,

2dBh=μ0hdyj

dB=μ0dyj2

B=0BdB= yμ0dyj2y μ0dyj2=μ0j2y+d2d2+y

B=μ0jy

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