Magnetic Field Strength Help (page 2)
The overall magnitude of a magnetic field is measured in units called webers , symbolized Wb. A smaller unit, the maxwell (Mx), is sometimes used if a magnetic field is very weak. One weber is equivalent to 100 million maxwells. Thus 1 Wb = 10 8 Mx, and 1 Mx = 10 −8 Wb.
The Tesla And The Gauss
If you have a permanent magnet or electromagnet, you might see its “strength” expressed in terms of webers or maxwells. More often, though, you’ll hear or read about units called teslas (T) or gauss (G). These units are expressions of the concentration, or intensity, of the magnetic field within a certain cross section. The flux density , or number of “flux lines per unit cross-sectional area,” is a more useful expressions for magnetic effects than the overall quantity of magnetism. Flux density is customarily denoted B in equations. A flux density of 1 tesla is equal to 1 weber per meter squared (1 Wb/m 2 ). A flux density of 1 gauss is equal to 1 maxwell per centimeter squared (1 Mx/cm 2 ). It turns out that the gauss is equivalent to exactly 0.0001 tesla. That is, 1 G = 10 −4 T, and 1 T = 10 4 G. To convert from teslas to gauss (not gausses!), multiply by 10 4 ; to convert from gauss to teslas, multiply by 10 −4 .
If you are confused by the distinctions between webers and teslas or between maxwells and gauss, think of a light bulb. Suppose that a lamp emits 20 W of visible-light power. If you enclose the bulb completely, then 20 W of visible light strike the interior walls of the chamber, no matter how large or small the chamber. However, this is not a very useful notion of the brightness of the light. You know that a single bulb gives plenty of light for a small walk-in closet but is nowhere near adequate to illuminate a gymnasium. The important consideration is the number of watts per unit area . When we say the bulb gives off a certain number of watts of visible light, it’s like saying a magnet has an overall magnetism of so many webers or maxwells. When we say that the bulb produces a certain number of watts per unit area, it’s analogous to saying that a magnetic field has a flux density of so many teslas or gauss.
The Ampere-turn And The Gilbert
When working with electromagnets, another unit is employed. This is the ampere-turn (At). It is a unit of magnetomotive force . A wire bent into a circle and carrying 1 A of current produces 1 At of magnetomotive force. If the wire is bent into a loop having 50 turns, and the current stays the same, the resulting magnetomotive force becomes 50 times as great, that is, 50 At. If the current in the 50-turn loop is reduced to 1/50 A or 20 mA, the magnetomotive force goes back down to 1 At.
A unit called the gilbert is sometimes used to express magnetomotive force. This unit is equal to about 1.256 At. To approximate ampere-turns when the number of gilberts is known, multiply by 1.256. To approximate gilberts when the number of ampere-turns is known, multiply by 0.796.
Flux Density Versus Current
In a straight wire carrying a steady direct current surrounded by air or by free space (a vacuum), the flux density is greatest near the wire and diminishes with increasing distance from the wire. You ask, “Is there a formula that expresses flux density as a function of distance from the wire?” The answer is yes. Like all formulas in physics, it is perfectly accurate only under idealized circumstances.
Consider a wire that is perfectly thin, as well as perfectly straight. Suppose that it carries a current of I amperes. Let the flux density (in teslas) be denoted B . Consider a point P at a distance r (in meters) from the wire, as measured along the shortest possible route (that is, within a plane perpendicular to the wire). This is illustrated in Fig. 14-3. The following formula applies:
B = 2 × 10 −7 ( I/r )
In this formula, the value 2 can be considered mathematically exact to any desired number of significant figures.
As long as the thickness of the wire is small compared with the distance r from it, and as long as the wire is reasonably straight in the vicinity of the point P at which the flux density is measured, this formula is a good indicator of what happens in real life.
Fig. 14-3 . Flux density varies inversely with the distance from a wire carrying direct current.
Magnetic Field Strength Practice Test
What is the flux density in teslas at a distance of 20 cm from a straight, thin wire carrying 400 mA of direct current?
First, convert everything to units in the International System (SI). This means that r = 0.20 m and I = 0.400 A. Knowing these values, plug them directly into the formula:
B = 2 × 10 −7 (I/r)
= 2.00 × 10 −7 (0.400/0.20)
= 4.0 × 10 −7 T
In the preceding scenario, what is the flux density B gauss (in gauss) at point P ?
To figure this out, we must convert from teslas to gauss. This means that we must multiply the answer from the preceding problem by 10 4 :
B gauss = 4.0 × 10 −7 × 10 4
= 4.0 × 10 −3 G
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