Electrostatics of Conductors, Electrostatic shielding, Voltage inside a spherical shell, E perpendicular to the surface, E at the surface. Quiz1

 

Worksheet:  Electrostatics of Conductors, Electrostatic shielding, Voltage inside a spherical shell, E perpendicular to the surface, E at the surface. Quiz1

🔹 Section A: Theory (Conceptual Questions)

Q1. What happens to excess charge placed on a conductor? Where does it reside?

Q2. Define electrostatic equilibrium.

Q3. What is the electric field inside a conductor in electrostatic equilibrium? Why?

Q4. Explain why electric field lines are always perpendicular to the surface of a conductor.

Q5. What is electrostatic shielding?

Q6. Why is the potential constant throughout a conductor?

Q7. What happens to the electric field at sharp edges of a conductor?

Q8. What is the electric field just outside a charged conductor?

Q9. What is the potential inside a charged spherical shell?

Q10. Give one real-life application of electrostatic shielding.

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🔹 Section B: Numerical Problems

Q11. A conductor carries a charge of $5 \times 10^{-6}\,C$. What is the electric field inside it?

Q12. The electric field just outside a conductor is $2 \times 10^5\,N/C$. Find the surface charge density.
$\varepsilon_0 = 8.85 \times 10^{-12}\,F/m$

👉 Use:
$E = \frac{\sigma}{\varepsilon_0}$

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Q13. A spherical conductor of radius $0.2\,m$ carries a charge $2 \times 10^{-6}\,C$. Find potential at the surface.

👉 Use:
$V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{R}$

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Q14. What is the potential at the center of the above sphere?

Q15. A hollow spherical conductor is charged. What is the electric field at a point inside the cavity?

Q16. A conductor has surface charge density $4 \times 10^{-6}\,C/m^2$. Find electric field just outside.

Q17. If electric field at surface is $10^6\,N/C$, find surface charge density.

Q18. A conductor is placed in an external electric field. What is the field inside it?

Q19. A charged spherical shell has potential $100\,V$. What is the potential at any point inside?

Q20. A Gaussian surface lies entirely inside a conductor. What is the flux through it?

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✅ Answer Key

Section A

1. On surface
2. No net motion of charges
3. Zero
4. Otherwise charges move
5. Protection from external fields
6. No electric field inside
7. Field is high
8. $E = \sigma/\varepsilon_0$
9. Constant (same as surface)
10. Faraday cage, cable shielding

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Section B

11. $E = 0$
    
12. $1.77 \times 10^{-6}\,C/m^2$
    
13. $9 \times 10^4\,V$
    
14. $9 \times 10^4\,V$
    
15. Zero
16. $4.52 \times 10^5\,N/C$
    
17. $8.85 \times 10^{-6}\,C/m^2$
    
18. Zero
19. $100\,V$
    
20. Zero

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✏️ Detailed Solutions

Q3. Why electric field inside conductor is zero?

Free electrons rearrange themselves such that they cancel any internal field → equilibrium → $E = 0$.

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Q4. Why E is perpendicular to surface?

If there were a tangential component → charges would move → violates equilibrium → hence perpendicular.

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Q8. Electric field just outside conductor

$$E = \frac{\sigma}{\varepsilon_0}$$

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Q11.

Inside conductor:

$$E = 0$$

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Q12.

$$\sigma = \varepsilon_0 E = (8.85 \times 10^{-12})(2 \times 10^5) = 1.77 \times 10^{-6}\,C/m^2$$

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Q13.

$$V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{R} = 9 \times 10^9 \cdot \frac{2 \times 10^{-6}}{0.2} = 9 \times 10^4\,V$$

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Q14.

Inside spherical conductor:

$$V = \text{constant} = V_{\text{surface}} = 9 \times 10^4\,V$$

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Q15.

Electric field inside cavity:

$$E = 0$$

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Q16.

$$E = \frac{\sigma}{\varepsilon_0} = \frac{4 \times 10^{-6}}{8.85 \times 10^{-12}} = 4.52 \times 10^5\,N/C$$

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Q17.

$$\sigma = \varepsilon_0 E = 8.85 \times 10^{-12} \times 10^6 = 8.85 \times 10^{-6}\,C/m^2$$

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Q18.

Field inside conductor:

$$E = 0$$

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Q19.

Potential inside shell:

$$V = \text{constant} = 100\,V$$

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Q20.

Using Gauss law:

$$\Phi = \frac{Q_{\text{enclosed}}}{\varepsilon_0} = 0$$