0

Question : An infinitely long, very thin cylindrical conducting tube of radius b carries a uniform surface current Js = azJs(A/m). Find B everywhere.

When r<b, it says that "In condition flux density of cylindrical conducting tube is 0 because the cylindrical tube has no internal surface. So when the condition the flux density is 0."

: Why there is no internal surface?

Sky Choi
  • 31
  • 2

2 Answers2

2

There is no magnetic flux density or magnetic field inside the conductor since the current only flows through the surface. Consider a closed circular path (L) concentric with the wire with radius \$r, r<b\$, by Ampere Circuital Law: $$\int_L \vec{B}.\vec{dl} = \mu I,$$ Here \$I\$ is the current which crosses the surface bounded by path L. Since there is no current inside the conductor \$I = 0\$.
By symmetry, $$\int_L \vec{B}.\vec{dl} = B(2\pi r) = 0 \implies B = 0.$$

sarthak
  • 3,766
  • 5
  • 19
  • 31
0

Why there is no internal surface?

Well of course there is so, the explanation in your 2nd paragraph is either wrong, misleading or, you have misinterpreted it.

Basically there can be no self-enclosing magnetic field lines on one side of a current carrying conductor (cylindrical or otherwise). Magnetic field lines (that are produced by current in the conductor) must enclose or encircle the whole conductor. They cannot do that inside the open area of the tube therefore they can't exist therefore there can be no magnetic field inside the tube: -

enter image description here

Picture from here.

Andy aka
  • 456,226
  • 28
  • 367
  • 807
  • I think I misunderstood the explanation. I thought the internal surface itself doesn't exist. So, the surface exsits, but magnetic flux density is not cuz it's zero... do I understand correctly? – Sky Choi Jun 16 '20 at 16:45
  • @SkyChoi it's a current tube so there is an internal surface. All tubes have internal surfaces. It's just one of those things about tubes/pipes/tunnels etc.. – Andy aka Jun 16 '20 at 16:53
  • Current flowing in a tube does not create a magnetic field inside the pipe/tube/tunnel. – Andy aka Jun 16 '20 at 17:00
  • Thank you for the perfect explanation! It's clear enough to make a dummy like me understand this haha thank uuu – Sky Choi Jun 16 '20 at 17:17
  • @SkyChoi please also note that will be magnetic field lines inside the conducting part of the tube despite what the other answer says. It won't be as high as the magnetic field outside the tube but it will exist and become zero at the inner surface of the tube. – Andy aka Jun 16 '20 at 17:20
  • @Andyaka I don't think there will be magnetic field inside if the wire is infinitely long with only surface current. The figure you draw for the solid wire assumes the current is uniformly distributed across the cross section of the wire. In this case I agree the magnetic field will vary linearly with the distance from centre. – sarthak Jun 16 '20 at 17:29