A long solenoid with radius 'a' and 'n' turns per unit length carries a time-dependent current [itex]I(t)[/itex] in the [itex]\phi[/itex] direction. Find the electric field (magnitude and direction) at a distance 's' from the axis (both inside and outside the solenoid), in quasi-static approximation.(adsbygoogle = window.adsbygoogle || []).push({});

What's quasi-static approximation? Anyway, without much prior thought I applied the flux rule :

[tex]\varepsilon = \int \vec E \cdot d\vec l = -{d\Phi \over dt}[/tex]

[itex]\vec B = \mu_0 nI \hat z[/itex], [itex]\vec A = \pi a^2 \hat z[/itex]

[tex]\Phi = \mu_0 nI \pi a^2[/tex]

[tex]\int \vec E \cdot d\vec l =-{d ( \mu_0 nI \pi a^2)\over dt}[/tex]

[tex]E2\pi a = -( \mu_0 n \pi a^2){dI\over dt}[/tex]

Before I proceed to the final step, someone please check my work.

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# Electric field of a solenoid

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