Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Magnetic field and

All moving charged particles produce magnetic fields. Moving point charges, such as electrons, produce complicated but well known magnetic fields that depend on the charge, velocity, and acceleration of the particles.

Magnetic field lines form in concentric circles around a cylindrical current-carrying conductor, such as a length of wire. The direction of such a magnetic field can be determined by using the "right hand grip rule" (see figure at right). The strength of the magnetic field decreases with distance from the wire. (For an infinite length wire the strength decreases inversely proportional to the distance.)

Bending a current-carrying wire into a loop concentrates the magnetic field inside the loop while weakening it outside. Bending a wire into multiple closely spaced loops to form a coil or "solenoid" enhances this effect. A device so formed around an iron core may act as an electromagnet, generating a strong, well-controlled magnetic field. An infinitely long cylindrical electromagnet has a uniform magnetic field inside, and no magnetic field outside. A finite length electromagnet produces a magnetic field that looks similar to that produced by a uniform permanent magnet, with its strength and polarity determined by the current flowing through the coil.

The magnetic field generated by a steady current ${I}$ (a constant flow of electric charges in which charge is neither accumulating nor depleting at any point)[nb 12] is described by the Biot–Savart law:

$mathbf{B} = frac{mu_0I}{4pi}intfrac{doldsymbol{ell} imes mathbf{hat r}}{r^2},$

where the integral sums over the wire length where vector d is the direction of the current, μ0 is the magnetic constant, r is the distance between the location of d and the location at which the magnetic field is being calculated, and is a unit vector in the direction of r.

A slightly more general[17][nb 13] way of relating the current ${I}$ to the B-field is through Ampère's law:

$oint mathbf{B} cdot doldsymbol{ell} = mu_0 I_{mathrm{enc}},$

where the line integral is over any arbitrary loop and ${I}$enc is the current enclosed by that loop. Ampère's law is always valid for steady currents and can be used to calculate the B-field for certain highly symmetric situations such as an infinite wire or an infinite solenoid.

In a modified form that accounts for time varying electric fields, Ampère's law is one of four Maxwell's equations that describe electricity and magnetism.

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