Em 11
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CHAPTER 11 DIMENSIONS Although we have not yet met all of the quantities in use in electricity and magnetism, we have met most of the important ones. Of those yet to come, some, such as impedance and reactance, will obviously have the dimensions of resistance; some, such as reluctance and permeance, you will rarely come across; and some, such as magnetic susceptibility, will obviously be dimensionless. Now is therefore quite a convenient time to gather together the various quantities we have come across, together with their dimensions (i.e. the powers of M, L, T and Q of which they are composed) and their SI units. It will be a good time, too, for the reader to review the definitions of the various quantities and to verify, from their definitions, their dimensions. Let me know if you find any mistakes in the following table.
M Force Work, energy Torque Power Linear momentum, impulse Rotational inertia Angular momentum Electric charge Electric dipole moment Current Potential difference Resistance Resistivity Conductance Conductivity Capacitance Electric field E Electric field D Electric flux ΦE Electric flux ΦD Permittivity Magnetic field B Magnetic field H Magnetic flux ΦB Magnetic flux ΦH Permeability Magnetic vector potential Inductance
Powers of L T Q
1 1 1 2 1 2 1 2 1 1 1 2 1 2 0 0 0 1 0 0 1 2 1 2 1 3 −1 −3 −1 −4 −1 −2 1 1 0 −2 1 3 0 0 −1 −3 1 0 0 −1 1 2 0 3 1 1 1 1 1 2
−2 −2 −2 −3 −1 0 −1 0 0 −1 −2 −1 −1 1 1 2 −2 0 −2 0 2 −1 −1 −1 −1 0 −1 0
0 0 0 0 0 0 0 1 1 1 −1 −2 −2 2 2 2 −1 1 1 1 2 −1 1 −1 1 −2 −1 −2
SI unit N J Nm W kg m s−1 or N s kg m2 Js C Cm A V Ω Ωm S S m−1 F N C−1 or V m−1 C m−2 Vm C F m−1 T A m−1 T m2 or V s Am H m−1 Tm H
M Force Work, energy Torque Power Linear momentum, impulse Rotational inertia Angular momentum Electric charge Electric dipole moment Current Potential difference Resistance Resistivity Conductance Conductivity Capacitance Electric field E Electric field D Electric flux ΦE Electric flux ΦD Permittivity Magnetic field B Magnetic field H Magnetic flux ΦB Magnetic flux ΦH Permeability Magnetic vector potential Inductance
Powers of L T Q
1 1 1 2 1 2 1 2 1 1 1 2 1 2 0 0 0 1 0 0 1 2 1 2 1 3 −1 −3 −1 −4 −1 −2 1 1 0 −2 1 3 0 0 −1 −3 1 0 0 −1 1 2 0 3 1 1 1 1 1 2
−2 −2 −2 −3 −1 0 −1 0 0 −1 −2 −1 −1 1 1 2 −2 0 −2 0 2 −1 −1 −1 −1 0 −1 0
0 0 0 0 0 0 0 1 1 1 −1 −2 −2 2 2 2 −1 1 1 1 2 −1 1 −1 1 −2 −1 −2
SI unit N J Nm W kg m s−1 or N s kg m2 Js C Cm A V Ω Ωm S S m−1 F N C−1 or V m−1 C m−2 Vm C F m−1 T A m−1 T m2 or V s Am H m−1 Tm H
