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Unformatted text preview: limits of integration from ∞ to - ∞ : B = dB = = = Since I , x and c are constants, we may remove them from the integral, simplifying the calculus. This integral is still quite complicated, and we must use a table of integration to solve it. It turns out that the integral is equal to . We evaluate this expression using our limits: B = When we plug infinity into our expression we find that l , implying that plugging in a value of infinity yields the value 1/ x 2 . When we plug in our negative infinity, we get -1/ x 2 in a similar manner. Thus: B = - = This is the equation we saw earlier for the field of a straight wire, implying that our calculus equation derived earlier is correct. The math that accompanies this kind of calculation is difficult, and rarely used, but it is essential for deriving the formulae we will encounter in the next section ....
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- Fall '10