Second: According to Faraday's law, if it is possible to envelop the conductor with a coil, then, you could measure a voltage induced at the loose extremes of the coil by varying the orientation of the conductor relative to the coil.
But, what kind of experiment do you want to perform?
I want to describe this phenomenon for undergraduate students as simple as possible. I am looking for simplest way to explain that this field exists inside a high-voltage conductor.
Dear Iman Sadeghkhani, Once it is a law ( Faraday's law), then there is no question of proving that. Yes, one can try to disprove which is impossible. You can give the examples of motors, generators, coils, transformers. Also, students are performing many experiments on magnetic circuits and calculating flux and flux density related ideas. So, when students are taking high voltage they are matured in basics of electrical circuit theory and technology.
My advice is if your students did not performed those experiments then you should put one lab experiment as LAB 0 for magnetic circuit in your High Voltage course.
in your question you say: " ... prove that magnetic field exists inside a high-voltage conductor"
First of all, it is necessary to observe that a magnetic field is generated by a current not by a voltage... So, in an open circuit (for example) the magnetic field inside and outside the conductor is zero, once the current is also zero. In this way, the conductor may stay at high voltage and not produce any magnetic field...
A possible experiment to demonstrate the existence of a magnetic field inside a conductor consists in prepare a conductive and transparent liquid solution and put this solution in a transparent cilindric vessel. In the bottom of this vessel you should to install a disc shaped non-magnetic electrode which is conected to a power supply. Another non-magnetic disc shaped electrode should be installed in the cover of the vessel (in way to touch the solution's surface) and conected to the other pole of power supply. Then, put a little waterproof compass in the solution as far as possible the axis of the vessel (on the axis the magnetic field is zero). It is expected that the compass indicate the presence of the magnetic field inside the conductive solution when you turn on the power supply.
In short Erick Arguello is correct. If one has studied the laws of inductance then you know that magnetic material in close proximity of a charged conductor will revel the flow. i.e fine magnetic material.
the idea suggested by Erick is correct and works well... But the problem is that Iman would demonstrate the presence of the magnetic field INSIDE the conductor. The experiment proposed by Erick demonstrates the magnetic field OUTSIDE the coductor once the conductor is "enveloped by the coil"... As in the experiment I suggested, the conductor is the liquid solution and the field indicator (compass) is put inside it. This experiment in not so difficult to perform. The solution may be NaCl in water.
Dear Iman Sadeghkhani, Get the following experimental setup to prove that Magnetic field exist around the current carrying conductor.
Apparatus:
one 9 V battery with holder
two hookup wires with alligator clips
compass
stop watch
Method:
Connect your wires to the battery leaving one end of each wire unconnected so that the circuit is not closed.
Be sure to limit the current flow to 10 seconds at a time (Why you might ask, the wire has very little resistance on its own so the battery will go flat very quickly). This is to preserve battery life as well as to prevent overheating of the wires and battery contacts.
Place the compass close to the wire.
Close the circuit and observe what happens to the compass.
Reverse the polarity of the battery and close the circuit. Observe what happens to the compass.
Conclusions:
Does a current flowing in a wire generate a magnetic field?
Is the magnetic field present when the current is not flowing?
Does the direction of the magnetic field produced by a current in a wire depend on the direction of the current flow?
How does the direction of the current affect the magnetic field?
most, at least freshmen consider the conductor surrounded by a dielectric in a dry or room temp environment i.e. a piece of paper with wire running through it and current also. Magnetic fibers will show confirmation by rule of thumb especially if coiled. ever player old school football with aluminum foil and magnets.
Thanks for your detailed answers. As I want to describe this phenomenon for undergraduate students, some simple approaches like picture of previous answer can better convince them.
Magnetic field doesn't exist inside a conductor but it exists around a current carrying conductor.
You may use a cardboard sheet and make a central hole into it and pass the conductor straight through that hole. Place some fine iron filings on the board. Switch on the H.V supply. You will see that the filings get arranged in definite patterns around the conductor.
This actually happens due to the arrangement of the filings along the magnetic lines of force around the current carrying H.V conductor.
This experiment is safe as you need not go closer to the apparatus (to view the patterns) and as you are using a bad conductor of current (cardboard).
I think it could exist! You see, when you have an energized coil which envelops a metal core, the magnetic field lines will tend to converge and go through the core.
And you're right, when a current flows through a conductor wire, a magnetic field will be generated outside,... but also inside! Remember the Ampere's Law (see the attachment)