1. Tardigrade
  2. Question
  3. Physics
  4. Let E 1( r ), E 2( r ) and E 3( 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

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Q. Let $E _{1}( r ), E _{2}( r )$ and $E _{3}( r )$ be the respective electric fields 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 $E_{1}\left(r_{0}\right)=E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right)$ at a given distance $r_{0}$, then

JEE AdvancedJEE Advanced 2014Electric Charges and Fields

Solution:

$\frac{ Q }{4 \pi \varepsilon_{0} r _{0}^{2}}=\frac{\lambda}{2 \pi \varepsilon_{0} I _{0}}=\frac{\sigma}{2 \varepsilon_{0}}$
$E _{1}\left(\frac{ r _{0}}{2}\right)=\frac{ Q }{\pi \varepsilon_{0} I _{0}^{2}}, $
$E _{2}\left(\frac{ r _{0}}{2}\right)=\frac{\lambda}{\pi \varepsilon_{0} I _{0}},$
$ E _{3}\left(\frac{ r _{0}}{2}\right)=\frac{\sigma}{2 \varepsilon_{0}}$
$\therefore E _{1}\left(\frac{ r _{0}}{2}\right) $
$=2 E _{2}\left(\frac{ r _{0}}{2}\right)$