Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is (σ/2ε0 ) nˆ , where nˆ is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.

 Q 1.29: A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is \left (\frac{\sigma}{2 \epsilon_{0}} \right ) \widehat{n} , where \widehat{n} is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.

Answers (1)

best_answer

Let the surface area of the sphere be S.

And assume that the hole is filled. For a point B, just above the hole, considering a Gaussian surface passing through B, we have

\oint E.dS = q/\epsilon_{0} 

Now, Since the electric field is always perpendicular to the surface of the conductor.

\\ \therefore \oint E.dS = E.S= q/\epsilon_{0} = (\sigma.S)/\epsilon_{0} \\ \implies E = \sigma/\epsilon_{0}

Using Superposition principle,  E =E_{1} + E_{2} ,

where E_{1} is due to the hole and  E_{2} is due to the rest of the conductor. (Both pointing outwards, i.e away from the centre)

Again, for point A, just below the hole, the Electric field will be zero because of electrostatic shielding.

Using the superposition principle, this will be due to E_{1}  pointing inwards(towards the centre) and due to E_{2}(Pointing away from the centre)

 0 =E_{1}-E_{2}  \implies E_{1}=E_{2} 

Using this relation, we get:

E =E_{1} + E_{2} = 2E_{1} \implies E_{1} = E/2 = \sigma/2\epsilon_{0}

Since this is pointing outwards, 

\boldsymbol{E_{1}} = \sigma/2\epsilon_{0}\ \boldsymbol{\widehat{n}}   it is the electric field in the hole.

(Trick: 1. Assume the hole to be filled.

            2. Consider 2 points just above and below the hole.

            3. Electric fields at these points will be due to the hole and the rest of the conductor. Use the superposition principle.)

Posted by

HARSH KANKARIA

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question