Any moving charge, whether a single electron traveling through space or a current through a conductive material, creates a **magnetic field**.^{3} The SI unit for magnetic field strength is the tesla (T). Because any moving charge creates a magnetic field, we would certainly expect that a collection of moving charge, in the form of a current through a conductive wire, would produce a magnetic field in its vicinity. The configuration of the magnetic field lines surrounding a current-carrying wire will depend on the shape of the wire.^{3} For an *infinitely long and straight current-carrying wire*, we can calculate the magnitude of the magnetic field produced by the current *I* in the wire at a perpendicular distance, *r*, from the wire as:

where B is the magnetic field at a distance, r, from the wire, and µ0 is the permeability of free space (4π x 10^{-7} T.m/A) and I is the current. The equation demonstrates an inverse relationship between the magnitude of the magnetic field and the distance from the current. Straight wires create magnetic fields in the shape of concentric rings. To determine the direction of the field vectors, use the **right-hand rule**. Point your thumb in the direction of the current and wrap your fingers around the current-carrying wire. Your fingers then mimic the circular field lines, curling around the wire.^{3} For a *circular loop of current-carrying wire of radius r,* the magnitude of the magnetic field at the center of the circular loop is given as:

The two equations are quite similar, the obvious difference being that the equation for the magnetic field at the center of the circular loop of wire does not include the constant *π*. The less obvious difference is that the first expression gives the magnitude of the magnetic field at any perpendicular distance, *r*, from the current-carrying wire, while the second expression gives the magnitude of the magnetic field only at the center of the circular loop of current-carrying wire with radius *r*.^{3}

Magnetic fields exert forces only on other moving charges. That is, charges do not “sense” their own fields; they only sense the field established by some external charge or collection of charges. Therefore, in our discussion of the magnetic force on moving charges and on current-carrying wires, we will assume the presence of a fixed and uniform external magnetic field. Note that charges often have both electrostatic and magnetic forces acting on them at the same time; the sum of these electrostatic and magnetic forces is known as the **Lorentz force**.^{3} When a charge moves in a magnetic field, a **magnetic force** may be exerted on it, the magnitude of which can be calculated as follows:

## F_{B} = qvB sinθ

where *q* is the charge, *ν* is the magnitude of its velocity, *B* is the magnitude of the magnetic field, and *θ* is the smallest angle between the vector **v** and the magnetic field vector **B**. The magnetic force is a function of the sine of the angle, which means that the charge must have a perpendicular component of velocity in order to experience a magnetic force. If the charge is moving parallel or antiparallel to the magnetic field vector, it will experience no magnetic force. Remember that sin 0° and sin 180° equal zero. This means that any charge moving parallel or antiparallel to the direction of the magnetic field will experience no force from the magnetic field. A second **right-hand rule** can be used here. To determine the direction of the magnetic force on a moving charge, first position your right thumb in the direction of the velocity vector. Then, put your fingers in the direction of the magnetic field lines. Your palm will point in the direction of the force vector for a positive charge, whereas the back of your hand will point in the direction of the force vector for a negative charge. A current-carrying wire placed in a magnetic field may also experience a magnetic force. For a straight wire, the magnitude of the force created by an external magnetic field, *F*_{B}, is:

*F*_{B} = ILB sinθ

_{B}= ILB sinθ

where *I* is the current, *L* is the length of the wire in the field, *B* is the magnitude of the magnetic field, and *θ* is the angle between **L** and **B**. The same right-hand rule can be used for a current-carrying wire in a field as for a moving point charge; just remember that current is considered the flow of positive charge.

__References__

1) Matthew Sadiku (2009). Elements of electromagnetics. p. 104.

2) Farago, P.S. (1961) An Introduction to Linear Network Analysis, pp. 18–21, The English Universities Press Ltd.

3) Keithley, Joseph F (1999). Daniell Cell. John Wiley and Sons. pp. 49–51.

4) Verschuur, Gerrit L. (1993). Hidden Attraction: The History and Mystery of Magnetism. New York: Oxford University Press. p. 76

5) Dorland’s (2012). Dorland’s Illustrated Medical Dictionary (32nd ed.). Elsevier Saunders.

p.1862.

6) Black, J.A., Sontheimer, H., Oh, Y., and Waxman, S.G. (1995). In The Axon, S. Waxman, J. Kocsis, and P. Stys, eds. Oxford University Press, New York, pp. 116–143.