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):     \(\lambda=\frac{1\times9\times10^4NC^{-1}\times0.02}{18\times10^9Nm^2C^{-2}}=10^{-7}Cm^{-1}\)