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Well... When the back emf is equal to the voltage supplied by the battery, it is not really hard or anything counter intuitive to realize how the current exists in such a case. See, all you need to realize is what is actually the back emf? When the charges in motion, tries to pass through an inductor - the inductor converts its kinetic energy into magnetic ...


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If the emf due to the solenoid is assumed to oppose the applied voltage and have equal magnitude (in volts), there is zero electromotive intensity in the wire. Since current is assumed to be present, this means the current flows even while total electromotive force vanishes. This is possible for wire made of perfect conductor (superconductor). In practice, ...


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The inductance of a coaxial cable does depend on the number of coils. But in addition to that, a coaxial cable will have a nonzero inductance even if it is perfectly straight, because there is a magnetic field inside the cable whenever it is carrying current, and this takes energy to set up, so you cannot instantaneously increase the current from zero to $I$ ...


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Short answer: it depends on the impedance of the load attached to the secondary coil. A perfect transformer can be modeled as a pair of inductors with mutual inductance $M$ and self-inductances $L_1$ and $L_2$, with $M^2 = L_1 L_2$. Denote the voltage across coil 1 and the current through it as $V_1(t) = \tilde{V}_1 e^{i \omega t}$ and $I_1(t) = ...


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The voltage between a and b is$IR=πr^2α/4.$ this is trivial it is a quarter of the Voltage. The Electric field is not generated from the $-∇V$ but from $-dA/dt $



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