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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electric field of a solenoid

**Physics Forums | Science Articles, Homework Help, Discussion**