\(\mathrm F=\;\frac1{4\mathrm\pi{\mathrm\varepsilon}_0}\frac{\mathrm Q\mathrm q}{\mathrm r^2}\)
\(\mathrm F=\) force, \(\frac1{4\mathrm\pi{\mathrm\varepsilon}_\mathrm o}=\) Coulomb constant
\(\left(9\;\times\;10^9\;\mathrm N\;\mathrm m^2\;\mathrm C^{-2}\right)\), \(\mathrm q\;=\) charge on the first object, \(\mathrm Q\;=\) charge on the second object, \(\mathrm r\;=\) separation between the charges
\(\mathrm E=\frac{\mathrm F}{\mathrm q}=\frac1{4\mathrm\pi{\mathrm\varepsilon}_0}\frac{\mathrm q}{\mathrm r^2}\)
\(\mathrm E\;=\) electric field strength, \(\mathrm F\;=\;\) force, \(\mathrm q\;=\) charge, \(\mathrm r\;=\) distance from the charge, \(\;\frac1{4\mathrm\pi{\mathrm\varepsilon}_\mathrm o}=\) Coulomb constant
\(\left(9\;\times\;10^9\;\mathrm N\;\mathrm m^2\;\mathrm C^{-2}\right)\)
\(\mathrm V=\frac{\mathrm\Delta\mathrm U}{\mathrm q}\)
\(\mathrm V\;=\) electrical potential difference, \(\mathrm\Delta\mathrm U\;=\) change in potential energy, \(\mathrm q\;=\) charge
\(\mathrm B=\frac{µ_\mathrm o\mathrm I}{2\mathrm\pi\mathrm r}\)
\(\mathrm B\;=\) magnetic flux density, \(\mathrm I\;=\) current in wire, \(\mathrm r\;=\) distance from the centre of the wire, \(\;\frac{µ_\mathrm o}{2\mathrm\pi}=\) magnetic constant
\(\text{(2 × }10^{-7}\text{T }\text{A}^{-1}\text{m)}\)
For a straight, current carrying wire perpendicular to a magnetic field \(\mathrm F=\mathrm B\mathrm I\mathrm l\)
\(\mathrm B\;=\) magnetic flux density, \(\mathrm F=\) force on the wire, \(\mathrm l=\) l=length of wire in the magnetic field, \(\mathrm I\) = current in the wire
For a charge moving perpendicular to a magnetic field \(\mathrm F=\mathrm q\mathrm v\mathrm B\)
\(\mathrm F=\) force on a charge moving in an applied magnetic field, \(\mathrm q\;=\) charge, \(\mathrm v=\;\) velocity of the charge, \(\mathrm B\;=\) magnetic flux density
\(\mathrm\phi=\mathrm B{\mathrm A}_\perp\)
\(\mathrm\phi=\;\) magnetic flux, \({\mathrm A}_\perp=\;\) area of current loop perpendicular to the applied magnetic field, \(\mathrm B\;=\) magnetic flux density
\(\mathrm e\mathrm m\mathrm f=-\;\frac{\mathrm n\bigtriangleup(\mathrm B{\mathrm A}_\perp)}{\operatorname\Delta\mathrm t}=-\;\mathrm n\frac{\operatorname\Delta\mathrm\phi}{\operatorname\Delta\mathrm t}\)
\(\mathrm e\mathrm m\mathrm f=\) induced potential difference, \(\triangle\mathrm\phi\;=\) change in magnetic flux, \(\mathrm n\;=\) number of windings in the loop, \({\mathrm A}_\perp=\;\) area of current loop perpendicular to the applied magnetic field, \(\operatorname\Delta\mathrm t\;=\) time interval over which the magnetic flux change occurs, \(\mathrm B\;=\) magnetic flux density
\(\frac{{\mathrm V}_\mathrm p}{{\mathrm V}_\mathrm s}=\frac{{\mathrm n}_\mathrm p}{{\mathrm n}_\mathrm s}\)
\({\mathrm V}_\mathrm p=\) potential difference across the primary coil, \(\;{\mathrm V}_\mathrm s=\;\) Vs= potential difference across the secondary coil, \({\mathrm n}_\mathrm p\;=\) number of turns on primary coil, \({\mathrm n}_\mathrm s=\) number of turns on secondary coil
\({\mathrm I}_\mathrm p{\mathrm V}_\mathrm p={\mathrm I}_\mathrm s{\mathrm V}_\mathrm s\;\)
\({\mathrm I}_\mathrm p=\) current in primary coil, \({\mathrm V}_\mathrm p=\;\) Vp= potential difference across primary coil, \({\mathrm I}_\mathrm s\) = current in secondary coil, \(\;{\mathrm V}_\mathrm s\) = potential difference across secondary coil