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# Magnetic Field Strength Help (page 2)

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By McGraw-Hill Professional
Updated on Sep 7, 2011

## 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

#### Problem 1

What is the flux density in teslas at a distance of 20 cm from a straight, thin wire carrying 400 mA of direct current?

#### Solution 1

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

#### Problem 2

In the preceding scenario, what is the flux density B gauss (in gauss) at point P ?

#### Solution 2

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

Practice problems of these concepts can be found at: Magnetism Practice Test

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