Electrostatics 1 Question 15

16. 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

(2014 Adv.)

(a) Q=40πr02

(b) r0=λ2πσ

(c) E1(r0/2)=2E2(r0/2)

(d) E2(r0/2)=4E3(r0/2)

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Answer:

Correct Answer: 16. (a)

Solution:

  1. Q4πε0r02=λ2πε0r0=σ2ε0Q=2πσr02

(a) is incorrect, r0=λπσ

(b) is incorrect, E1r02=4E1(r0)

As E11r2

E2r02=2E2(r0) as E21r

(c) is correct

E3r02=E3(r0)=E2(r0)

as E3r0(d) option is incorrect



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