Connection Between Magnetism and Electric Current

Magnetism and Electric Currents

• The connection between electricity and magnetism was discovered accidentally by the Danish scientist Hans Christian Oersted (1777–1851) in 1820.
• Oersted was giving a science lecture when he closed a switch and allowed a current to flow through a wire. He noticed that a nearby compass needle rotated rapidly when the switch was closed.
• With that simple observation, Oersted discovered that electric currents can create magnetic fields.

Magnetism and Electric Currents

• To visualize the magnetic field produced by a wire, consider a long, straight wire that carries a current, I.
• Shaking iron filings onto a sheet of paper that is pierced by the wire results in a circular pattern of filings centered on the wire (see figure (a) below). Clearly, the magnetic field "circulates" around the wire.

Magnetism and Electric Currents

• We can gain additional information about the magnetic field by placing a group of small compasses about the wire, as in figure (b) below.

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• In addition to confirming the circular shape of the field lines, the compass needles show the field's direction.

Magnetism and Electric Currents

• To understand this direction, we use the magnetic field right-hand rule (RHR):

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• This rule is illustrated by the compass needles in the figure on the next slide.

Magnetism and Electric Currents

• As the figure indicates, to find the direction of the field, point the thumb of the right hand in the direction of the current, I. The fingers then curl in the direction of the magnetic field, B.

Magnetism and Electric Currents

• In some cases a magnetic field will point into or out of the page. This can be difficult to draw. Therefore, we establish the convention that the symbol ⊗ indicates that the magnetic field points into the page.
• The way to remember this is to think of a magnetic field vector as an arrow. At the end of the arrow are crossed feathers. Therefore, if you view a vector from behind, it looks like an X.

Magnetism and Electric Currents

• Similarly, if the arrow points out of the page, all you will see is the point at its tip. Thus, we represent a magnetic field vector pointing out of the page with the symbol ⊙, where the dot represents the tip of the arrow.

Magnetism and Electric Currents

• Experiments show that the magnetic field produced by a current-carrying wire doubles if the current, I, doubles. In addition, the field doubles if the radial distance from the wire, r, is halved.
• These observations are summarized in one statement: The magnetic field produced by a current in a wire is proportional to the current and inversely proportional to the radial distance from the wire.

Magnetism and Electric Currents

• The magnetic field for a long, straight wire is given by the following equation:

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• In this equation, µ₀, is a constant called the permeability of free space. Its value is

µ₀ = 4π x 10⁻⁷ T·m/A

Magnetism and Electric Currents

• The following example shows how to use the magnetic field equation.

Magnetism and Electric Currents

• The following example illustrates how the total magnetic field is found when two current-carrying wires contribute to the field.

Magnetism and Electric Currents

• You've seen that a long, straight wire carrying an electric current produces a magnetic field. What happens if a straight wire is wrapped into a circular loop instead?
• Figure (a) below shows a wire loop connected to a battery producing a current in the direction indicated.

Magnetism and Electric Currents

• Using the magnetic field RHR, as shown in the figure, we see that the magnetic field points from left to right as it passes through the loop.
• Notice also that the field lines are bunched together within the loop, indicating that the field is intense there. The field lines are more widely spaced outside the loop, where the field is weaker.
• The most interesting aspect of the field produced by the current-carrying loop is its close resemblance to the field of a bar magnet, as is illustrated in figure (b) on the next slide.

Magnetism and Electric Currents

• Notice that one side of the loop behaves like a north magnetic pole (with field lines exiting) and the other side like a south magnetic pole (with field lines entering).

Magnetism and Electric Currents

• When two loops with identical currents are placed next to one another, the force between loops will be similar to the force between two bar magnets pointing in the same direction (see figure below).

Magnetism and Electric Currents

• As you can see, the ghosted bar magnets would attract one another, since their opposite poles are near one another.
• Therefore, wires with currents in the same direction experience an attractive force.
• As figure (b) below indicates, wires with currents in opposite directions experience a repulsive force.

Magnetism and Electric Currents

• A solenoid is an electrical device in which a long wire is wound into a succession of closely spaced loops—forming a cylindrical coil of wire.
• A solenoid carrying an electric current produces an intense, nearly uniform magnetic field inside the loops, as indicated in the figure below.

Magnetism and Electric Currents

• For this reason, solenoids are commonly referred to as electromagnets.
• Notice that each loop of a solenoid carries a current in the same direction. It follows that the magnetic field between loops is attractive and serves to hold them tightly together.
• The magnetic field lines in the previous figure are tightly packed inside the solenoid but are widely spaced outside. In the case of a very long, tightly packed solenoid, the magnetic field is intense and uniform inside the solenoid.

Magnetism and Electric Currents

• If a solenoid has N loops and length L, the magnetic field inside the solenoid is given by the following equation:

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• Notice that the result is independent of the cross-sectional area of the solenoid and that the field depends directly on the number of loops per unit length and on the current.

Magnetism and Electric Currents

• When used as an electromagnet, a solenoid has many useful properties.
• A solenoid produces a strong magnetic field that can be turned on or off at the flip of switch—unlike the field of a permanent magnet.
• The magnetic field of a solenoid can be intensified by filling the core of the solenoid with an iron bar. In such a case, the magnetic field of the solenoid magnetizes the iron bar, and its field adds to that of the solenoid.

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