Chapter 19. Magnitude of magnetic field due to a long, straight wire (19-9)

Question

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Question

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Question

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{"title":"Magnitude of the magnetic field due to a long, straight wire","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,47,37,98\"}]"} {"title":"Permeability of free space","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"116,15,156,62\"}]"} {"title":"Current in the wire","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"171,8,199,52\"}]"} {"title":"Distance from the wire to the location where the field is measured","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"179,104,205,137\"}]"}

Question

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Review

Equation 19-9 and the field properties shown in Figure 19-17 are strictly correct only if the wire is infinitely long. But they are very good approximations if the distance \(r\) is small compared to the length of the wire.

The constant \(\mu_0\) in Equation 19-9, called the permeability of free space for historic reasons, plays a role in magnetism that’s comparable to the role of the constant \(\epsilon_0\), the permittivity of free space, in electricity (see Section 16-6). Its value is exactly \(\mu_0 = 4\pi \times 10^{-7}\ \mathrm{T} \cdot \mathrm{m}/\mathrm{A}\).