Biot-Savart Law - Electromagnetics - Unanswered Questions!

[Jackson1928]

Hi I need help!

I have a few holes in my Electromagnetics Knowledge which I'd like to plug!

The Biot-Savart Law states that the Electromagnetic Field (H) measured at a diatance (r) falls by 1/2Π (Pie). The full equation is given by H=I/2 Πr, I is the current flowing in a straight line conductor. The field strength is given in A/m (Amps Per Metre)

Here are my questions;

1. Is the Biot-Savart Law applicable to Magnetic fields produced by DC and AC Currents? I.e a battery and and alternating current.

2. Let us assume that I have dialled in some figures and I find that at 1 metre from a straight line power conductor (AC or DC), the field strength is 100A/m. At this measurement point there is a steel plate which is grounded, how can I calculate the current flowing in the plate that has ben induced by the magnetic field?

I appreciate that for AC Mag Fields, Impedance etc may fare in the equations and also resistivity, however I am just looking for a general equation if possible.

The problem I am trying to solve is on a railway. A DC conductor rail is about 0.5m away from metal infrastructure and I wich to be able to confirm that the Biot-Savaty equation works for AC/DC electrification and also get some kind of idea of what current may be induced. I am assuming that a Mag Field generated by a DC source will induce a DC current and Vice-versa.

I know this is such a basic question to some readers. however I have not been able to find these questions and answers in any books or through on-line research.

I could really do with an answer ASAP.

Many Thanks - Jackson 1928

 

[jimmy neutron]

Re: Biot-Savart Law - Electromagnetics - Unanswered Question

I don't think I can help too much, though can hopefully shed some light on your problem:

1) The Biot Savart Law is only strictly true for time steady currents. When you look at currents that change in time you have to take into account fields that are referred to as "retarded". This is because the changes in electric and magnetic fields only travel at a finite speed, namely the speed of light, c. However, for circuits that are small in size and for low frequencies, people usually ignore retardation effects (referred to as the "quasi-static approximation").

2) This probably has to be done numerically unless there are some special assumptions that you can make, eg the steel plate is of infinite extent, it has a special set up with respect to the current flowing in the conductor. You don’t specify many details about the steel plate.

>I am assuming that a Mag Field generated by a DC source will induce a DC .
>current and Vice-versa.
3) If the current is DC then the magnetic field may be influenced by the position of the steel plate , but no current will be induced since currents are only induced by changing magnetic fields. It may be that you are thinking of the transitory currents that flow when (eg) the current through the conductor is first switched on or when the steel plate is first brought near to the curremt carrying conductor.

Sorry I couldn't have given some of the answers you want,

Jim

 

[neils_arm_strong]

Current wont flow in the steel plate. I think only changing magnetic fields (AC) can produce AC electric fields. I am not sure of the situation in DC magnetic field.

 

[jimmy neutron]

Re: Biot-Savart Law - Electromagnetics - Unanswered Question

If the magnetoc field is truly static then no current will be induced in the steel plate. However I wasn't sure if Jackson 1928 was looking at a situation when the magnetic field was first turned on or if the plate was being brought close to the magnetic field. In both cases the steel plate will feel the influence of a changing magnetic field and a transistory current will flow.

However, as you say, a DC field will not induce a Dc current.