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Let E1(r), E2(r) and E3(r) be the respec...

Let `E_1(r)`, `E_2(r)` and `E_3(r)` be the respectively electric field at a distance r from a point charge `Q`, an infinitely long wire with constant linear charge density `lambda`, and an infinite plane with uniform surface charge density `sigma`. If `E_1(r_0)=E_2(r_0)=E_3(r_0)` at a given distance `r_0`, then

A

`Q = 4 sigma r_(0)^(2)`

B

`r_(0) = (lambda)/(2 pi r)`

C

`E_(1) (r_(0)//2) = 2E_(2) (r_(0)//2)`

D

`E_(2) (r_(0) //2) = 4E_(a) (r_(0)//2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(Q)/(4 pi epsi_(0) r_(0)^(2)) = (lambda)/( 2 pi epsi_(0) r_(0)) = (sigma)/(2 epsi_(0)) rArr q = 2 pi sigma r_(0)^(2)`
(A) is incorrect `r_(0) = (lambda)/( pi simga )` and (B) is incorrect ` E_(1) ((r_(0))/(2)) = 4E_(1) (r_(0))`
As , `E_(1) prop (1)/(2) rArr E_(2) (r_(0))/(2)) = 2 E_(2)(r_(0)) as E_(2) prop (1)/(r)`
(C) is correct `E_(1)((r_(0))/(r_(0))` . As `E_(0) prop rArr ` (D) is incorrect .
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