Abstract
From our detailed consideration of induction in moving conductors, we became aware of the existence of the Lorentz force
(F for example in newton (=1 N), B in V s/m2 (=1 T), u in m/s, Q in A s).
This force acts on a charge Q which is moving at the velocity u in a magnetic field of flux density B. As can be seen from the vector product, the force is perpendicular both to the magnetic field and to the velocity of the charge (Fig. 8.1).
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Notes
- 1.
W. Weber and R. Kohlrausch in 1856 described this velocity simply as a “critical” value which could make magnetic forces just as strong as electrical forces.
- 2.
The copper wires used in everyday house wiring are normally limited to current densities of less than 6 A/mm2. A copper wire with a cross-sectional area of 1 mm2 and a length of 1 m has a mass m = 8.95 g, and thus the amount of substance n = 0.14 mol (Vol. 1, Sect. 13.1). It contains copper ions, each carrying one positive electrical elementary charge. For these ions, the Faraday constant is the quotient
$$\displaystyle\frac{\text{Charge}\ Q}{\text{Amount of substance}\ n}=9.65\cdot 10^{4}\,\frac{\text{A\,s}}{\text{mol}}\,.$$The copper wire therefore contains a positive ionic charge of \(Q=1.36\cdot 10^{4}\) A s. The mobile negative charge Q between the lattice ions is just as large. Inserting this quantity of charge into Eq. (4.4) gives
$$\displaystyle u=\frac{I\,l}{Q}=\frac{6\,\text{A}\cdot 1\,\text{m}}{1{.}36\cdot 10^{4}\,\text{A\,s}}=4{.}4\cdot 10^{-4}\,\frac{\mathrm{m}}{\mathrm{s}}=0{.}44\,\frac{\mathrm{mm}}{\mathrm{s}}\,.$$ - 3.
This is not yet the “creeping” pointer setting; see below!
- 4.
- 5.
For bar magnets made of steel, which were formerly used extensively and can still be found today, the flux distribution is shown by the lower image in Fig. 8.18 . There, one can localize the poles N and S at the “centers” of the shaded areas. In the case of magnetic fields from flat current-carrying coils (as in the left-hand image in Fig. 8.14), one can no longer speak of poles at all.
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Lüders, K., Pohl, R.O. (2018). Forces in Magnetic Fields. In: Lüders, K., Pohl, R. (eds) Pohl's Introduction to Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-50269-4_8
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DOI: https://doi.org/10.1007/978-3-319-50269-4_8
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