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Magnetic Field Associated With a Current

Magnetic field associated with a current

If you hold a compass near a wire through which current isflowing, the needle on the compass will be deflected.

Since compasses work by pointing along magnetic field lines, this means that there must be a magnetic field near the wire through which the current is flowing.

The magnetic field produced by an electric current is alwaysoriented perpendicular to the direction of the current flow. Below is a sketch of what the magnetic field around a wire looks like when the wire has a current flowing in it. We use \(\vec{B}\) to denote a magnetic field and arrows on field lines to show the direction of the magnetic field.Note that if there is no current there will be no magnetic field.


The direction of the current in the conductor (wire) is shown by the central arrow. The circles are field lines and they also have a direction indicated by the arrows on the lines. Similar to the situation with electric field lines, the greater the number of lines (or the closer they are together) in an area the stronger the magnetic field.

Important: All of our discussion regarding field directions assumes that we are dealing with conventional current.

To help you visualise this situation, stand a pen or pencil straight up on a desk. The circles are centred around the pencil or pen and would be drawn parallel to the surface of the desk. The tip of the pen or pencil would point in the direction of the current flow.


You can look at the pencil or pen from above and the pencil or pen will be a dot in the centre of the circles. The direction of the magnetic field lines is counter-clockwise for this situation.

To make it easier to see what is happening we are only going to draw one set of circular fields lines but note that this is just for the illustration.


If you put a piece of paper behind the pencil and look at it from the side, then you would be seeing the circular field lines side on and it is hard to know that they are circular. They go through the paper. Remember that field lines have a direction, so when you are looking at the piece of paper from the side it means that the circles go into the paper on one side of the pencil and come out of the paper on the other side.


Whenwe are drawing directions of magnetic fields and currents, we usethe symbols \(\odot\) and \(\otimes\).The symbol \(\odot\) represents anarrow that is coming out of the page and the symbol \(\otimes\) represents an arrow that is going into the page.

It is easy to remember the meanings of the symbols if you think ofan arrow with a sharp tip at the head and a tail with feathers in the shape of a cross.



The Danish physicist, Hans Christian Oersted, was lecturing one day in 1820 on the possibility of electricity and magnetism being related to one another, and in the process demonstrated it conclusively with an experiment in front of his whole class. By passing an electric current through a metal wire suspended above a magnetic compass, Oersted was able to produce a definite motion of the compass needle in response to the current. What began as a guess at the start of the class session was confirmed as fact at the end. Needless to say, Oersted had to revise his lecture notes for future classes. His discovery paved the way for a whole new branch of science – electromagnetism.

We will now look at three examples of current carrying wires. For each example we will determine the magnetic field and draw the magnetic field lines around the conductor.

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