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An infinite line charge produces an electric field of 9×10⁴ N/C at a distance of 2 cm. Then the linear charge density will be ________. (K = 9 × 10⁹ Nm²/C²)

Asked in GUJCET 2024 · Charged cylinder and line charge

• (1) 10 μC/m
• (2) 1 μC/m
• (3) 0.01 μC/m
• (4) 0.1 μC/m

Step-by-step solution

Why the other options are wrong

• (1) Leaves the distance in centimetres, using r = 2 in place of 0.02 m: λ = (Er)/(2K) = (9×10⁴×2)/(1.8×10¹⁰) = 10⁻⁵ C/m = 10 μC/m, a hundred times too big.
• (2) Converts 2 cm to 0.2 m, dividing by 10 instead of 100: λ = (9×10⁴×0.2)/(1.8×10¹⁰) = 10⁻⁶ C/m = 1 μC/m, ten times too big.
• (3) Converts 2 cm to 0.002 m, dividing by 1000 instead of 100: λ = (9×10⁴×0.002)/(1.8×10¹⁰) = 10⁻⁸ C/m = 0.01 μC/m, ten times too small.

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