Question

Find linear charge density if infinite line charges produce a field of 9 x 104 and the distance is 2 cm.

Answer 1

Step 1: Electric field due to infinite line charge
Electric field due to infinite line charge is given by:
$E=\frac{\lambda}{2\pi\epsilon_0d}$
⇒ $\lambda=2\pi\epsilon_0Ed$ …….....(1)
Where λ is the linear charge density and d is the perpendicular distance of a point from the infinite line charge.
**Step 2: Substituting the values **
∵$\frac{1}{4\pi\epsilon_0}=9\times10^9Nm^2C^{-2}$
⇒ $2\pi\epsilon_0=\frac{1}{18\times10^9Nm^2C^{-2}}$
From Eq (1): $\lambda=\frac{1\times9\times10^4NC^{-1}\times0.02}{18\times10^9Nm^2C^{-2}}=10^{-7}Cm^{-1}$