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- Thread starter Silviu
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You are right if the problem was asking for the **exact analytical solution** for the current density then you would need to solve a system of partial differential equations (apply Maxwell's equation's in differential form with the boundary conditions imposed by this problem and then solve them, my guess is that the system of PDE's gonna be very hard and we can hope only for numerical solutions). (or another method would be to solve an ODE for each solenoid as you said, we would have infinitely many ODE's and they would be coupled due to mutual induction between the solenoids but that's another story).

BUT the problem doesn't ask for the exact analytical solution, it just asks for the**next order (of ##\omega##) correction** to the current density j. In other words it asks for an approximation solution that gives the j up to the first two orders of ##\omega##, while from taylor's series we know that j will probably contain more orders, possibly infinite.

BUT the problem doesn't ask for the exact analytical solution, it just asks for the

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Thanks a lot! I feel stupid now for asking this...You are right if the problem was asking for theexact analytical solutionfor the current density then you would need to solve a system of partial differential equations (apply Maxwell's equation's in differential form with the boundary conditions imposed by this problem and then solve them, my guess is that the system of PDE's gonna be very hard and we can hope only for numerical solutions).

But the problem doesn't ask for the exact analytical solution, it just asks for thenext order (of ##\omega##) correctionto the current density j. In other words it asks for an approximation solution that gives the j up to the first two orders of ##\omega##, while from taylor's series we know that j will probably contain more orders, possibly infinite.

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