Magnetism and magnetic effects of electric current Formula Sheet

Magnetic Dipole Moment: \(p_m = q_m \times 2l\) (\(p_m\): dipole moment, \(q_m\): pole strength, \(2l\): magnetic length)
Coulomb's Inverse Square Law of Magnetism: \(F = k \frac{q_{mA} q_{mB}}{r^2}\) (\(F\): force, \(k\): constant \(\mu_0 / 4\pi\), \(q_{mA}, q_{mB}\): pole strengths, \(r\): distance)
Magnetic Field along Axial Line: \(B_{axial} = \frac{\mu_0}{4\pi} \frac{2p_m}{r^3}\) (\(B\): magnetic induction, \(\mu_0\): permeability of free space, \(r\): distance)
Magnetic Field along Equatorial Line: \(B_{equatorial} = \frac{\mu_0}{4\pi} \frac{p_m}{r^3}\) (symbols as above)
Torque on a Bar Magnet: \(\tau = p_m B \sin\theta\) (\(\tau\): torque, \(B\): external magnetic field, \(\theta\): angle of orientation)
Potential Energy of a Dipole: \(U = -p_m B \cos\theta\) (\(U\): potential energy)
Magnetic Susceptibility: \(\chi_m = \frac{M}{H}\) (\(\chi_m\): susceptibility, \(M\): intensity of magnetization, \(H\): magnetizing field)
Biot-Savart Law: \(dB = \frac{\mu_0}{4\pi} \frac{I\,dl \sin\theta}{r^2}\) (\(dB\): small magnetic field, \(I\): current, \(dl\): length element)
Field due to a Long Straight Wire: \(B = \frac{\mu_0 I}{2\pi a}\) (\(a\): perpendicular distance from the wire)
Ampere's Circuital Law: \(\oint B \cdot dl = \mu_0 I_{enclosed}\) (\(I_{enclosed}\): net current threading the closed loop)
Field inside a Solenoid: \(B = \mu_0 n I\) (\(n\): number of turns per unit length)
Magnetic Lorentz Force: \(F = q(v \times B)\) (\(q\): charge, \(v\): velocity)
Cyclotron Frequency: \(f = \frac{qB}{2\pi m}\) (\(f\): frequency, \(m\): mass of the particle)
Force on a Current-Carrying Conductor: \(F = B I l \sin\theta\) (\(l\): length of the conductor)

Magnetism and magnetic effects of electric current - Formula Sheet

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