Question

# An infinite line charge produces a field of $$9\times 10^{4}$$N/C at a distance of 2 cm. Calculate the linear charge density.

Solution

## $$\textbf{Step 1: Electric field due to infinite line charge}$$ Electric field due to infinite line charge is given by:   $$E = \dfrac{\lambda}{2\pi \in_0 d}$$    $$\Rightarrow \lambda = 2\pi \in_0 E \ d$$                                  $$....(1)$$Where $$\lambda$$ is the linear charge density and $$d$$ is the perpendicular distance of point from the infinite line charge.$$\textbf{Step 2: Substituting the values }$$                     $$\because \dfrac{1}{4\pi \in_0} = 9 \times 10^9 Nm^2C^{-2}$$  $$\Rightarrow 2\pi \in_0 = \dfrac{1}{18\times 10^9 Nm^2C^{-2}}$$From Eq $$(1):$$     $$\lambda = \dfrac{1 \times 9 \times 10^4\ NC^{-1}\times 0.02m}{18\times 10^9\ N m^2 C^{-2} }= 10^{-7}\ Cm^{-1}$$PhysicsNCERTStandard XII

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