Let E1(r), E2(r) and E3(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density s. If E1(r0) = E2(r0) = E3(r0) at a given distance r0, then

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Physics

Electric Field and Charged Particle in Electric Field

Question

Let E₁(r), E₂(r) and E₃(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density s. If E₁(r₀) = E₂(r₀) = E₃(r₀) at a given distance r₀, then

$r_{0} = \frac{λ}{2 πσ}$

E₂ (r₀/2) = 4E₃(r₀/2)

E₁(r₀/2) = 2E₂ (r₀/2)

Q = 4σπr₀²

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$E_{1} (\frac{r_{0}}{2}) = \frac{Q}{4 {πε}_{0} {(r_{0} / 2)}^{2}}$

$2 E_{2} (\frac{r_{0}}{2}) = \frac{2 λ}{2 π ε_{0} (r_{0} / 2)}$

(D) $E_{2} (\frac{r_{0}}{2}) = \frac{λ}{2 π ε_{0} (r_{0} / 2)}$

$4 E_{3} (\frac{r_{0}}{2}) = \frac{4 σ}{2 ε_{0}}$