# Magnetic Field of a Straight Current

#### Quiz

Quiz 1. How can you make a magnet out of a long strand of wire and an iron bar?

a. Attach the wire to either end of the bar, and send a current through it.
b. Send a current through the bar.
c. Spin the bar over the wire as a current runs through it.
d. Wrap the wire around the bar, and send a current through it.

The wire wrapped around the bar will induce a magnetic field in the bar when a current passes through the wire.

#### Magnetic Field of a Straight Current Simulation

When the next simulation is not visible, please refer to the following link.

Magnetic Field around an Electric Current
The first evidence for the existence of a magnetic field around an electric current was observed in 1820 by Hans Christian Oersted (1777-1851). He found that a wire carrying current caused a freely pivoted compass needle in its vicinity to be deflected. If the current in a long straight wire is directed from C to D, as shown in Fig1, a compass needle below it, whose initial orientation is shown in dotted lines, will have its north pole deflected to the left and its south pole deflected to the right.

Fig 1.  Oersted's experiment. Compass needle is deflected toward the west when the wire CD carrying current is placed above it and the direction of the current is toward the north, from C to D.

If the current in the wire is reversed and directed from D to C, then the north pole will be deflected to the right, as seen from above. In terms of the forces acting on the poles, these forces are clearly perpendicular to the direction of the current and to the line from the nearest portion of the wire to the pole itself.

Fig 2. Pattern formed by iron filings showing the circular magnetic field around a wire carrying current.

The magnetic field in the neighborhood of a wire carrying current can be investigated either by exploring the region with a small compass or by using iron filings. When a wire carrying current is passed perpendicularly
through a plane board and iron filings are sprinkled on the board, the filings form a circular pattern, as shown in Fig2. Thus the magnetic field generated by the wire carrying current is circular in a plane at right angles to the current. The circles are concentric, with their common center at the position of the wire. The direction of the magnetic field can be determined with the aid of a small compass.

Fig 3. Direction of the magnetic field around a wire (a) when the current is out of the paper; (b) when the current is into the paper. The dot represents a head-on view of an arrow while the cross represents a rear view.

If we look along the wire so that the current is coming toward us, the magnetic field is counterclockwise. If we draw a dot to represent a head-on view of an arrow and a cross to represent a rear view of an arrow, we may show the direction of the magnetic field, associated with current in a wire perpendicular to the plane of the paper when the current is coming toward the reader in Fig 3(a), and when the current is away from the reader in Fig 3(b). A small compass placed anywhere in the field will orient itself tangent to one of these circles with its north pole in the direction of the arrow.

Fig4. (a) When the wire carries a strong current, the alignments of the iron filings show that the magnetic field induced by the current forms concentric circles around the wire. (b) Compasses can be used to show the direction of the magnetic field induced by the wire.

A long, straight, current-carrying wire has a cylindrical magnetic field
The experiment shown in Fig4 (a) uses iron filings to show that a current-carrying conductor produces a magnetic field. In a similar experiment, several compass needles are placed in a horizontal plane near a long vertical wire, as illustrated in Fig4 (b). When no current is in the wire, all needles
point in the same direction (that of Earth’s magnetic field). However, when the wire carries a strong, steady current, all the needles deflect in directions tangent to concentric circles around the wire. This result points out the direction of B, the magnetic field induced by the current. When the current is reversed, the needles reverse direction.

The right-hand rule can be used to determine the direction of the magnetic field
These observations show that the direction of B is consistent with a simple rule for conventional current, known as the right-hand rule: If the wire is grasped in the right hand with the thumb in the direction of the current, as shown in Fig5, the four fingers will curl in the direction of B.

Fig5. You can use the righthand rule to find the direction of this magnetic field.

As shown in Fig4 (a), the lines of B form concentric circles about the wire. By symmetry, the magnitude of B is the same everywhere on a circular path centered on the wire and lying in a plane perpendicular to the wire. Experiments show that B is proportional to the current in the wire and inversely proportional to the distance from the wire.