TABLE 36.1 Units in Magnetism Symbol cgs Units x Factor SI units B=H+4TM Magnetic flux density B tesla(T), wb/m2 maxwell (Mx) webers(wb) magnetomotive force) UHM 10/4兀 (Oe) Magnetization(per volume) Magnetization(per mass Magnetic moment xKμμ sss xxxxxxxx dimensionless dimensionless 4π Wb/A·m Permeability(material) Wb/A Bohr m =0.927×10erg/Oex103 Am Demagnetizing factor n dimensionless 14 dimensionless tic flux density In the case of electric fields there is in addition to E an electric flux density field d, the lines of which be on positive charges and end on negative charges. D is measured in coulombs per square meter and is associated with the electric field E(V/m)by the relation D=EE E where e, is the permittivity of free space(E,=8.854 x 10-12 F/m)and E, is the(dimensionless)dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m2)=A,u, H, where u, is the permeability of free space(u,=4T X 10 H/m) andu, is the(dimensionless)permeability. In contrast to the lines of the D field, lines of B are closed, having no beginning or ending. This is not surprising when we remember that while lated positive and negative charges exist, no magnetic monopole has yet been discovered Relative permeabilities The range of the relative permeabilities covers about six orders of magnitude(Table 36. 2)whereas the range of dielectric constants is only three orders of magnitude Forces on a Moving Charge A charged particle, g, traveling with a velocity v and subjected to a magnetic field experiences a force This equation reveals how the Hall effect can be used to determine whether the majority current carriers sample of a semiconductor are(negatively charged) electrons flowing, say, in the negative direction or (positively charged)holes flowing in the positive direction. The(transverse)force( Fig. 36. 2)will be in the same direction in either case, but the sign of the charge transported to the voltage probe will be positive for holes and negative for electrons. In general, when both electric and magnetic fields are present, the force experienced by the carriers is given by F=q(E+v×B) The Hall effect is the basis of widely used and sensitive instruments for measuring the intensity of magnetic fields over a range of 10to2×10°A/m. e 2000 by CRC Press LLC© 2000 by CRC Press LLC Magnetic Flux Density In the case of electric fields there is in addition to E an electric flux density field D, the lines of which begin on positive charges and end on negative charges. D is measured in coulombs per square meter and is associated with the electric field E (V/m) by the relation D = er eoE where eo is the permittivity of free space (eo = 8.854 ¥ 10–12 F/m) and er is the (dimensionless) dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m2 ) = mrmoH, where mo is the permeability of free space (mo = 4p 2 10–7 H/m) and mr is the (dimensionless) permeability. In contrast to the lines of the D field, lines of B are closed, having no beginning or ending. This is not surprising when we remember that while isolated positive and negative charges exist, no magnetic monopole has yet been discovered. Relative Permeabilities The range of the relative permeabilities covers about six orders of magnitude (Table 36.2) whereas the range of dielectric constants is only three orders of magnitude. Forces on a Moving Charge A charged particle, q, traveling with a velocity v and subjected to a magnetic field experiences a force F = qv 2 B This equation reveals how the Hall effect can be used to determine whether the majority current carriers in a sample of a semiconductor are (negatively charged) electrons flowing, say, in the negative direction or (positively charged) holes flowing in the positive direction. The (transverse) force (Fig. 36.2) will be in the same direction in either case, but the sign of the charge transported to the voltage probe will be positive for holes and negative for electrons. In general, when both electric and magnetic fields are present, the force experienced by the carriers is given by F = q (E + v 2 B) The Hall effect is the basis of widely used and sensitive instruments for measuring the intensity of magnetic fields over a range of 10–5 to 2 2 106 A/m. TABLE 36.1 Units in Magnetism Quality Symbol cgs Units 2 Factor = SI units B = H + 4pM B = mo(H + M) Magnetic flux density B gauss (G) 2 10–4 = tesla (T), Wb/m2 Magnetic flux F maxwell (Mx) 2 10–8 = webers (Wb) G · cm2 Magnetic potential difference (magnetomotive force) U gilbert (Gb) 2 10/4p = ampere (A) Magnetic field strength H oersted (Oe) 2 103 /4p = A/m Magnetization (per volume) M emu/cc 2 103 = A · m Magnetization (per mass) s emu/g 2 1 = A · m2 /kg Magnetic moment m emu 2 10–3 = A · m2 Susceptibility (volume) c dimensionless 2 4p = dimensionless Susceptibility (mass) k dimensionless 2 4p = dimensionless Permeability (vacuum) mo dimensionless 2 4p.10–7 = Wb/A · m Permeability (material) m dimensionless 2 4p.10–7 = Wb/A · m Bohr magneton mB = 0.927 2 10–20 erg/Oe 2 10–3 = Am2 Demagnetizing factor N dimensionless 2 1/4p = dimensionless