Anonymous

# 普通物理 的問題!! 請幫幫我!!

" A metal tube has an inner radius a and outer radius b.

It carries a current I uniformly spread over its cross-sectional area.

Find the magnetic field at all points. "

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• Anonymous

We have to make use of the line integral as follows:

where B and l are the magnetic field and vector length of the chose path and Ienc is the amount of current enclosed by the path.

Then, we choose all paths circular being concentric with the inner and outer surfaces of the wire and lying in the same plane as the surfaces.

So for case (1), when radius of path < a:

Since no current is enclosed insude the path, Ienc = 0 and therefore B = 0.

Case (2), when a <= radius <= b:

Current density in the wire J = I/[π(b2 - a2)]

For any r within a and b, the current enclosed is:

Ienc = Jπ(r2 - a2)

= Iπ(r2 - a2)/[π(b2 - a2)]

= I(r2 - a2)/(b2 - a2)

Hence,

B 2πr = I(r2 - a2)/(b2 - a2)

B = (I/2πr) [(r2 - a2)/(b2 - a2)]

Case (3): When r > b

Just like ordinary equation: B = I/2πr

Source(s): My physics knowledge