Question

Which expression gives the electric field due to an infinite line charge?

Options

• \[E = \frac{\lambda}{4\pi\varepsilon_0 r^2}\]

• \[E = \frac{\lambda r}{2\pi\varepsilon_0}\]

• \[E = \frac{\lambda}{2\pi\varepsilon_0 r}\]

• \[E = \frac{\sigma}{2\varepsilon_0}\]

Answer 1

Using the cylindrical Gaussian surface gives \[E \cdot 2\pi r l = \lambda l/\varepsilon_0\]. Cancelling \[l\] yields \[E = \lambda/(2\pi\varepsilon_0 r)\].