Let , and be the respective electric field at a distance from a point charge , an…

PHYSICS · Single correct · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

Let E1(r)E_1(r) , E2(r)E_2(r) and E3(r)E_3(r) be the respective electric field at a distance rr from a point charge QQ , an infinitely long wire with constant linear charge density λ\lambda , and an infinite plane with uniform surface charge density σ\sigma . If E1(r0)=E2(r0)=E3(r0)E_1(r_0) = E_2(r_0) = E_3(r_0) at a given distance r0r_0 , then [Adv. 2014] (1) Q=4σπr02Q = 4\sigma\pi r_0^2 (2) r0=λ2πσr_0 = \frac{\lambda}{2\pi\sigma} (3) E1(r0/2)=2E2(r0/2)E_1(r_0/2) = 2E_2(r_0/2) (4) E2(r0/2)=4E3(r0/2)E_2(r_0/2) = 4E_3(r_0/2)

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