Question

The electric field due to an infinitely long thin wire with linear charge density \( \lambda \) at a radial distance \( r \) is proportional to:

• A. \(\frac{\lambda^2}{r}\)
• B. \(\frac{\lambda}{r}\)
• C. \(\frac{\lambda}{r^2}\)
• D. \(\frac{\sqrt{\lambda}}{\sqrt{r}}\)
• E. \(\frac{\lambda}{\sqrt{r}}\)

Hint:

Gauss's Law simplifies the calculation of electric fields when the symmetry of the charge distribution is high.

Answer 1

The Correct Option is B

The electric field \( E \) due to an infinitely long thin wire is given by Gauss's Law, which results in: \[ E = \frac{\lambda}{2\pi \epsilon_0 r} \] Hence, the electric field is proportional to \(\frac{\lambda}{r}\).