The dimension of the ratio of magnetic flux a | vedclass

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(B) We know that magnetic flux $\phi$ is related to current $I$ and inductance $L$ by the equation $\phi = L I$.According to Faraday's law of inductio

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charge

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(B) We know that magnetic flux $\phi$ is related to current $I$ and inductance $L$ by the equation $\phi = L I$.According to Faraday's law of induction,the induced $emf$ is given by $\epsilon = -\frac{d\phi}{dt}$.From Ohm's law,the current $I$ is given by $I = \frac{\epsilon}{R}$,where $R$ is the resistance.Substituting the expression for $\epsilon$,we get $I = \frac{1}{R} \frac{d\phi}{dt}$.Rearranging this,we have $I dt = \frac{d\phi}{R}$.Integrating both sides,we find that the ratio $\frac{\phi}{R}$ has the dimensions of $\int I dt$,which is the dimension of electric charge $(q = I 	imes t)$.Therefore,the dimension of $\frac{\phi}{R}$ is equal to that of charge.

The dimension of the ratio of magnetic flux and the resistance is equal to that of:

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