静磁気学 (Magnetostatics)

Ampere's force law

Fm=kmI1I2r=μ02πI1I2r F_m = k_m \frac{ I_1 I_2 }{r} = \frac{ {\mu}_0 }{ 2\pi } \frac{ I_1 I_2 }{ r }
F12=μ04πI1I2∮C1∮C2ds2×(ds1×r^12)r122 \mathbf{F}_{12} = \frac{\mu_0}{4 \pi} I_1 I_2 \oint_{C_1} \oint_{C_2} \frac {d \mathbf{s_2} \times (d \mathbf{s_1} \times \hat{\mathbf{r}}_{12} )} {r_{12}^2}

Biot-Savart Law

dB=μ04πIdl×rr3 d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{ I d\mathbf{l} \times \mathbf{r} }{ r^3 }

Ampere's circuital law

∮CB⋅dl=μ0∫∫SJf⋅dS=μ0Ienc \oint_C \mathbf{B} \cdot \mathrm{d} \mathbf{ l } = {\mu}_0 \int\!\!\!\int_S \mathbf{J_f} \cdot \mathrm{d}\mathbf{S} = {\mu}_0 \mathbf{ I }_{enc}
rotB=∇×B=μJf \mathrm{rot} \mathbf{B} = \nabla \times \mathbf{B} = {\mu} \mathbf{J}_f

Lorentz force

Fmag=q(v×B) \mathbf{F}_{mag} = q \left( \mathbf{v} \times \mathbf{B} \right)
F=q(E+v×B) \mathbf{F} = q \left( \mathbf{E} + \mathbf{v} \times \mathbf{B} \right)