22.9 Magnetic fields produced by currents: ampere’s law

Learning objectives

By the end of this section, you will be able to:

• Calculate current that produces a magnetic field.
• Use the right-hand rule 2 to determine the direction of current or the direction of magnetic field loops.

The information presented in this section supports the following AP® learning objectives and science practices:

• 2.D.2.1 The student is able to create a verbal or visual representation of a magnetic field around a long straight wire or a pair of parallel wires. (S.P. 1.1)
• 3.C.3.1 The student is able to use right-hand rules to analyze a situation involving a current-carrying conductor and a moving electrically charged object to determine the direction of the magnetic force exerted on the charged object due to the magnetic field created by the current-carrying conductor. (S.P. 1.4)
• 3.C.3.2 The student is able to plan a data collection strategy appropriate to an investigation of the direction of the force on a moving electrically charged object caused by a current in a wire in the context of a specific set of equipment and instruments and analyze the resulting data to arrive at a conclusion. (S.P. 4.2, 5.1)

How much current is needed to produce a significant magnetic field, perhaps as strong as the Earth’s field? Surveyors will tell you that overhead electric power lines create magnetic fields that interfere with their compass readings. Indeed, when Oersted discovered in 1820 that a current in a wire affected a compass needle, he was not dealing with extremely large currents. How does the shape of wires carrying current affect the shape of the magnetic field created? We noted earlier that a current loop created a magnetic field similar to that of a bar magnet, but what about a straight wire or a toroid (doughnut)? How is the direction of a current-created field related to the direction of the current? Answers to these questions are explored in this section, together with a brief discussion of the law governing the fields created by currents.

Magnetic field created by a long straight current-carrying wire: right hand rule 2

Magnetic fields have both direction and magnitude. As noted before, one way to explore the direction of a magnetic field is with compasses, as shown for a long straight current-carrying wire in [link] . Hall probes can determine the magnitude of the field. The field around a long straight wire is found to be in circular loops. The right hand rule 2 (RHR-2) emerges from this exploration and is valid for any current segment— point the thumb in the direction of the current, and the fingers curl in the direction of the magnetic field loops created by it.

Making connections: notation

For a wire oriented perpendicular to the page, if the current in the wire is directed out of the page, the right-hand rule tells us that the magnetic field lines will be oriented in a counterclockwise direction around the wire. If the current in the wire is directed into the page, the magnetic field lines will be oriented in a clockwise direction around the wire. We use $\odot$ to indicate that the direction of the current in the wire is out of the page, and $\otimes$ for the direction into the page.