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Electrostatics question

2019 · Q139
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Electrostatics question

2019 · Q139

NEETPhysicsElectrostaticsMCQ+4 / −1
A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre :
  1. A
    zero as r increases for r < R, decreases as r increases for r > R
  2. B
    zero as r increases for r < R, increases as r increases for r > R.
  3. C
    decreases as r increases for r < R and for r > R.
  4. D
    increases as r increases for r < R and for r > R.
View written solutionFree

Correct answer: A

For inside (r <\lt < R)

Apply, Gauss law,

∮Ein.dS→\oint {{E_{in}}} .\overrightarrow {dS} ∮Ein​.dS = qenε0{{{q_{en}}} \over {{\varepsilon _0}}}ε0​qen​​

⇒\Rightarrow⇒ Ein = 0 [ As qen = 0 ]

For outside (r >\gt > R)

∮E→out.dS→=qenε0\oint {{{\overrightarrow E }_{out}}} .\overrightarrow {dS} = {{{q_{en}}} \over {{\varepsilon _0}}}∮Eout​.dS=ε0​qen​​

Here, qen = Q

So, Eout.4π\pi πr2 = Qε0{Q \over {{\varepsilon _0}}}ε0​Q​

∴\therefore∴ Eout ∝\propto∝ 1r2{1 \over {{r^2}}}r21​

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