In the textbook University Physics, when talking about induction experiments of coil, one of the points made is:

If all these experiments are repeated with a coil that has the same shape but different material and different resistance, the current in each case is inversely proportional to the total circuit resistance. This shows that the induced EMFs that are causing the current do not depend on the material of the coil but only on its shape and the magnetic field.

I'm not sure I fully understand this. Isn't the resistance based on the resistivity of the material (therefore dependant on the material), length of the wire and cross-sectional area? Doesn't this mean that the material influences the resistance and therefore the induced current?


1 Answer 1


Yes, the induced emf is independent of the type of material used, but the induced current is dependent on the type of material used.

This is essentially from Faraday's Law: $$\varepsilon = -\frac{\text{d}\Phi_B}{\text{d}t} $$which shows that the induced emf is only depedent on the magentic flux linked through the loop, which implies that it depends on the magnetic field, the cross sectional area and the angle between $\vec B$ and $\vec A$.

For the induced current however: $$I = \frac{|\varepsilon|}{R}$$ and as $R = \rho l/A$, the induced current is dependent on the material used , and is only inversely proportional to the total resistance of the circuit (the value of $\varepsilon$ won't change unless the previously mentioned parameters change.)

Hope this helps.


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