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We seem to be interested only in B[=A(q/r^2)(v' cross ].What about E?Is it an electrostatic field?I suppose not.If not,then should be time dependent and del cross E=-(d/dt)B

Taking line integral of (1),W=integral(a to F.dr

=integral(a to E.dr + 0

Does this mean F(mag) is conservative?

if a and b are the same,Will W=0?

in that case will Lorentz force be conservative?

however, i saw in Griffiths's Quantum Mechanics that magnetic forces cannot be expressed like (-dV/dx) like other conservative forces.

what is the physics?