Register to reply

Magnetic field at the edges of a current-carrying wire

by Nikitin
Tags: currentcarrying, edges, field, magnetic, wire
Share this thread:
Nikitin
#1
Mar21-13, 05:16 AM
P: 619
At the edges of a very long current-carrying wire, the magnetic field is not the same as in the middle, right?

And integrating biot-savart's law in the edge-region of the wire will make it possible to calculate this field-strength, right?
Phys.Org News Partner Physics news on Phys.org
Mapping the optimal route between two quantum states
Spin-based electronics: New material successfully tested
Verifying the future of quantum computing
Philip Wood
#2
Mar21-13, 06:22 AM
PF Gold
P: 943
Yes. If you're interested in the field at a point P, which may be anywhere outside the wire, the B-S rule gives you the field at P due to each current element. You integrate these field contributions from the whole wire. This gives you (see thumbnail for meaning of symbols):
[tex]B = \frac{\mu_0 I}{4\pi a} [cos \theta_2 - cos \theta_1][/tex].

This covers the cases you're interested in; it's very general.

For a very long wire, if P is outside the wire, near the middle of the wire, then [itex]\theta_2 = 0[/itex], [itex]\theta_1 = \pi[/itex], so [itex]B = \frac{\mu_0 I}{2\pi a} [/itex], whereas if you're outside the wire, at the (left hand) end of the wire, [itex]\theta_2 = 0[/itex], [itex]\theta_1 = \frac{\pi}{2}[/itex], so [itex]B = \frac{\mu_0 I}{4\pi a} [/itex]. If you think about it, you would indeed expect the field to be half as much in the second case as in the first - if you appreciate that the exact length of the wire is immaterial in these 'long wire' examples, because the field from distant parts of the wire is negligible.

Remember that you can't, in practice, have a wire which carries a steady current and which has two free (unconnected) ends. The wire needs to be part of a circuit. For the second case above, the left hand end of the wire would have to be connected to the rest of a circuit by another wire. If this other wire went in the direction directly away from P it wouldn't contribute to the field at P. Can the rest of the circuit (apart from the straight wire) be made so as not to contribute to the field at P?
Attached Thumbnails
St wire B-S notation.jpg  
Nikitin
#3
Mar21-13, 03:46 PM
P: 619
thanks!


Register to reply

Related Discussions
Magnetic field caused by a current-carrying wire Introductory Physics Homework 6
Magnetic Field of a Straight Current-Carrying Wire Introductory Physics Homework 8
Torque of a current carrying wire in magnetic field Introductory Physics Homework 3
Infinite wire carrying current, magnetic field Introductory Physics Homework 10
Magnetic Field of current carrying straight wire Advanced Physics Homework 3