Permeability

Also called Vacuum permeability, mu naught, Magnetic constant

The constant describing how much magnetisation a material takes on in an external magnetic field. The vacuum value, mu naught, is 4 pi times 10 to the minus 7 tesla metres per ampere.

μ0=4π×107 (Tm)/A\mu_0 = 4\pi \times 10^{-7} \ (\mathrm{T}\cdot\mathrm{m})/\mathrm{A}

Printed in the Constants group of both the AP Physics 2 and the AP Physics C: Electricity and Magnetism sheets, and the magnetic counterpart of permittivity. As a decimal it is about 1.26×1061.26 \times 10^{-6}.

Leave it in the 4π4\pi form when you substitute. On the AP Physics 2 sheet it appears inside exactly one equation, B=μ0I/(2πr)B = \mu_0 I / (2\pi r), and there the π\pi cancels against the denominator, turning the whole constant into a factor of 2×1072 \times 10^{-7}. Converting to a decimal first buys an extra rounding step for nothing. The same cancellation runs through the Biot-Savart law, which arrives as μ0/4π\mu_0 / 4\pi already.

Every equation that builds a magnetic field from a current carries it: B=μ0I/(2πr)B = \mu_0 I/(2\pi r) for a straight wire, μ0Ienc\mu_0 I_{\text{enc}} in Ampere's law, μ0nI\mu_0 n I inside a solenoid.

For matter it is not a table lookup. The AP Physics 2 CED is unusually blunt here: the permeability of matter differs from that of free space, and it is not a constant for a material, varying with factors including temperature, orientation, and the strength of the external field. Density you can look up; this you cannot.

Do not confuse the symbol with the coefficient of friction, which also uses μ\mu, or the two constants with each other. Permittivity is electric and sits under 4π4\pi; permeability is magnetic and sits on top of it.

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