1)

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

   


A) Q=4σπr20

B) r0=λ2πσ

C) E1(r02)=2E2(r02)

D) E2(r02)=2E3(r02)

Answer:

Option C

Explanation:

Q4πϵ0r20=λ2πϵ0r0=σ2ϵ0

                          Q=2πσr20

 (a) is incorrect,   r0=λπσ

   (b)    is incorrect,   E1(r02)=4E1(r0)

 As,            E11r2

    E2(r02)=2E2(r0)     as    E21r

  (c) is correct.

    E3(r02)=E3(r0)=E2(r0)

 as          E3r0

  (d) is in correct.