Problem: Find the magnetic field due to a straight current segment of length .08800 m, at a distance of 7.7 meters from the segment, given that the vector from the segment to the point is perpendicular to the segment, and that a current of 6.4 Amps flows in the segment.
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Solution: The magnetic field is given by B=k'(IL)/r ^ 2. Here, I = 6.4 Amps, L= .08800 m, and r= 7.7 meters. Thus IL= .5632 Amp meters, and B = (.000000001000 Tesla / Amp meter)( .5632 Amp m)/( 7.7 m) ^ 2 = .000000000009499 Tesla.
Generalized Response: Just as the electric field strength E = k q / r^2 of a point charge q falls off as the inverse square of distance from the source q, the magnetic field B = k' (IL) / r^2 of a short charge-and-length segment IL falls of as the inverse square of its distance from the source IL. We consider IL to be the source of the magnetic field, just as q is the source of electric field.
The magnetic field is a little trickier than the electric field, since it depends not only on distance but on the orientation of the point with respect to the direction of the current I from which it arises. However if the orientation is such that a line from the source IL to the point is perpendicular to I, the equation B = k' (IL) / r^2 holds.
The direction of the magnetic field is found by the right-hand rule: if the fingers of the right hand are directed in the direction of the current, and oriented so that when the fingers are current they move toward the direction of the line from source to point, the thumb points in the direction of the magnetic field.
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Figure description: