According to standard electromagnetic theory, if the charge A is stationary and the charge B is moving along arbitrary trajectory then the electromagnetic force on charge A is: F⃗A=qA(−∇ϕ−∂∂tA⃗)\vec{F}_A = q_A \left(-\nabla\phi - \frac{\partial}{\partial t}\vec{A}\right) where ϕ\phi and A⃗\vec{A} are velocity dependent scalar and vector potentials (Lienard-Wiechert potentials), i.e. ϕ=14πϵqB∣r⃗A−r⃗B(tr)∣(1−n⃗B⋅β⃗B)A⃗=14πμv⃗BqB∣r⃗A−r⃗B(tr)∣(1−n⃗B⋅β⃗B).\phi = \frac{1}{4\pi\epsilon}\frac{q_B}{\left|\vec{r}_A-\vec{r}_B(t_r)\right|\left(1-\vec{n}_B\cdot\vec{\beta}_B\right)} \\ \vec{A} = \frac{1}{4\pi}\frac{\mu\vec{v}_B q_B}{\left|\vec{r}_A-\vec{r}_B(t_r)\right|\left(1-\vec{n}_B\cdot\vec{\beta}_B\right)}. where trt_r is retarded time. However, if charge A is moving and charge B is stationary, then according to standard electromagnetic theory, the force on charge A is Coulomb's force: F⃗A=−qA∇ϕ=−14πϵ∇qAqB∣r⃗A−r⃗B∣.\vec{F}_A = -q_A \nabla\phi = -\frac{1}{4\pi\epsilon}\nabla\frac{q_A q_B}{\left|\vec{r}_A-\vec{r}_B\right|}. However, to me this is not logical. The force on charge AA should be velocity-dependent even when charge BB is at rest and charge AA is moving. Does anyone have any ideas on this issue? Any papers or books in scientific literature which deal with this problem would be greatly appreciated as well.