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Homework Statement:
 We have an Ideal Solenoid with current ##I## and turn per length ##n## and a core with magnetic permittivity of ##\mu## is inside it like the figure. the length ##x_0## of solenoid has the core and the rest is empty. Find the Inductance of a Solenoid.
Relevant Equations:

##\int B ds = \mu I##, ##L_T = L_1 + L_2##
The question said the ##\mu## in question is the ##\mu## in the above equation so no need to worry about scale factor.
For finding magnetic field ##B##, We see this question like two Solenoids. for the first one, we have ##\int B ds = \mu I## so ##B x_0 = \mu I n x_0 ## so ##B = \mu n I##. For the second one we have ##B = \mu_0 n I##. For the Inductance we have ##L = \mu l n^2 A## so we have ##L_1 = \mu x_0 n^2 A## and for the second one we have ##L_2 = \mu_0 (Lx_0) n^2 A##. And the ##L_{total} = L_1 + L_2##
Is my reasoning right? I think I didn't considered mutual Inductance but the question is from an exam and it was orally said you don't need to consider mutual inductance.
Is my reasoning right? I think I didn't considered mutual Inductance but the question is from an exam and it was orally said you don't need to consider mutual inductance.