Please help in this potentiometer problem


How do I prove this? I am not getting any major ideas…

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Anyone?

the current through the galvanometer will be equal to the \displaystyle I = -\frac{1}{R }\frac{dФ}{dt}, so the charge going through the galvanometer will be equal \displaystyle q =\int^t_0 Idt= \frac{Ф}{R}. Then, by expressing the flux as \displaystyle Ф = \int Sn \vec B \vec {ds} and taking \displaystyle H=\frac{B}{\mu_0} we can obtain the needed equation.

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So yeah, I obtained the following

\frac{qR}{\mu_0} = \int_a^b \vec H_0 \cdot d\vec S,

but I’m so not sure that we can simply plug in d\vec S = S\cdot nd\vec l and assume that this is fine (chinese hieroglyphs at the end of the pic make me doubt even more.) Maybe this can be proved with the use of vector calculus?

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lol
thank you… :innocent:

Thanks a lot!