JEE Advanced | 2014ElectrostaticsHard

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 σ. If E1(r0) = E2(r0) = E3(r0) at a given distance r0, then

Options

A.Q = 4σπr02
B.r0 =
C.E1(r0/2) = 2E2(r0/2)
D.E2(r0/2) = 4E3(r0/2)

Solution

E1(r0) = , E1
E2(r0) =
E3(r0) = E3
Now, E1(r0) = E2(r0) = E3(r0)
⇒
⇒ Q = 2πr2σ
⇒ = σ or r =
E1 = 4E1(r0) = 2E2
Also, E2 = 2E3(r0) = 2E3
Only C is correct.

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