The electric field 0.400 m from a very long uniform line of charge is 840 n>c. The charge which contained in a 2.00 cm section line is 3.74 × 10⁻¹⁰ C.
Given,
Radius = 0.400 m,
Electric field = 840 N/C,
Length = 2.00 cm = 0.200 m,
Area = 2πrL ,
θ = 0°,
E₀ = 8.85 × 10⁻¹² C² / Nm²,
The charge that is contained in a 2.00 cm section of the line is given by the formula,
Ф = EAcosθ,
Ф = E · 2πrL · cosθ
Ф = (840 × 2π × 0.4 × 0.2) cos0°
Ф = 42.2 Nm² / C
∴ Ф = q / E₀
⇒ q = Ф × E₀,
⇒ q = 42.2 × 8.85 × 10⁻¹² C² / Nm²,
⇒ q = 3.74 × 10⁻¹⁰ C
Hence, the charge is q = 3.74 × 10⁻¹⁰ C.
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