Q. 234.3( 38 Votes )

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

Answer :

Given:

E = 9 × 10^{4} NC^{-1}

d = 2 cm

Let the linear charge density = λ Coulomb/metre

We know that, Electric field produced by a line charge with a linear charge density σ, at a distance d is given by,

…(1)

Where, λ = linear charge density.

ε_{0} = permittivity of free space

ε_{0} = 8.85 × 10^{-12}N^{-1} m^{-2}C^{2}

d = distance

From equation (1) we have,

⇒ λ = E × 2 × π × ε_{0} × d

⇒ λ = 9 × 10^{4} NC^{-1} × 2 × π × 8.85 × 10^{-12}N^{-1} m^{-2}C^{2} × 0.02m

⇒ λ = 10 ×10^{-8} Cm^{-1}

The linear charge density is 10^{-7} Cm^{-1}.

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PREVIOUSA uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m2. (a) Find the charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere?NEXTTwo large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10–22 C/m2. What is E: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?

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