An infinite plane sheet of charge having uniform surface charge density + σ s C / m 2 is placed on x − y plane. Another infinitely long line charge having uniform linear charge density + λ e C / m

Question

An infinite plane sheet of charge having uniform surface charge density $+ σ_{s} C / m^{2}$ is placed on $x - y$ plane. Another infinitely long line charge having uniform linear charge density $+ λ_{e} C / m$ is placed at $z = 4 m$ plane and parallel to $y$ -axis. If the magnitude values $∣ σ_{s} ∣ = 2 ∣ λ_{e} ∣$ then at point $(0, 0, 2)$ , the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $π n : 1$ . The value of $n$ is_______.

Question diagram: An infinite plane sheet of charge having uniform surface cha

Answer:

16.00

Solution:

$\frac{E _{S}}{E _{ℓ}} = \frac{σ}{2 ϵ _{0}} \times \frac{2 π ϵ _{0} r}{λ} = \frac{π \times σ r}{λ} = \frac{π \times 2 λ \times 2}{λ} = \frac{4 π}{1} ∴ n = 16$

TestHub · Accepted Answer

​ E ℓ ​ E S ​ ​ = 2 ϵ 0 ​ σ ​ × λ 2 π ϵ 0 ​ r ​ = λ π × σ r ​ = λ π × 2 λ × 2 ​ = 1 4 π ​ ∴ n = 16 ​

Physics - Elecrostatics Question with Solution | TestHub

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