Practice portal › Electric Charge and Properties › Field of Spheres, Shells and Cylinders

An infinite line charge produces a field of 9×10⁴ N C⁻¹ at a distance of 2 cm. Calculate the electric field produced at a distance of 3 cm.

Asked in GUJCET 2022 · Charged cylinder and line charge

Answer: (1) 6×10⁴ N C⁻¹

Step-by-step solution

Given: E₁ = 9×10⁴ N C⁻¹ at r₁ = 2 cm; find E₂ at r₂ = 3 cm.

Idea: the field of an infinite line charge is E = λ/(2πε₀ r), so E ∝ 1/r.

(E₂)/(E₁) = (r₁)/(r₂) = 2/3

E₂ = 9×10⁴×2/3 = 6×10⁴ N C⁻¹

Only the ratio of the distances enters, so the centimetres need not be converted. (The point-charge law 1/(r²) would give 4×10⁴, which is not offered: a line charge's field falls off more slowly.)

So the field at 3 cm is 6×10⁴ N C⁻¹.

Why the other options are wrong

More Field of Spheres, Shells and Cylinders questionsAll Field of Spheres, Shells and Cylinders questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer