Class 12th Physics Chapter-2 Notes on Electrostatics of Conductors – Detailed Explanation

 

First: What do we mean by “electrostatic situation”?

• Electrostatic situation means:

  • Charges are at rest

  • No current is flowing

  • The charge distribution is stable

In this situation, conductors show some very special properties.

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1. Electric field inside a conductor is zero

Explanation (step by step):

• Conductors have free electrons.

• If an electric field existed inside:

  • Free electrons would experience force $F=qE$

  • They would start moving → current would flow

• But electrostatics means no motion of charges.

So what happens?

• Charges redistribute themselves automatically

• This redistribution continues until the net electric field inside becomes zero

Conclusion:

$$\boxed{{\displaystyle E_{\text{inside conductor}}=0}}$$

📌 Very important line for exams:

“In electrostatic equilibrium, the electric field inside a conductor is zero because free charges rearrange themselves to cancel any internal field.”

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2. Electric field at the surface of a charged conductor is always normal

Why can’t it be tangential?

• Suppose electric field had a component along the surface

• Then surface charges would feel a force

• They would start moving along the surface

• This violates the static condition

So:

• Tangential component = zero

• Only perpendicular (normal) component exists

Conclusion:

Electric field at the surface of a charged conductor is always perpendicular to the surface

📌 Exam phrase:

“In electrostatic equilibrium, the electric field at the surface of a conductor has no tangential component.”

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3. Interior of a conductor cannot have excess charge

Use Gauss’s Law

Take:

• A small imaginary Gaussian surface inside the conductor

We know:

• $E=0$ inside conductor

• Electric flux $=\oint \vec{E}\cdot d\vec{S}=0$

By Gauss’s law:

$$\oint \vec{E}\cdot d\vec{S}=\frac{q_{\text{enclosed}}}{{\epsilon }_0}$$

So:$$q_{\text{enclosed}}=0$$

Meaning:

• No net charge exists inside

• Any extra charge must move to the surface

Conclusion:

$$\boxed{{\displaystyle \text{Excess charge resides only on the surface}}}$$

📌 Common mistake:
Students say “charges move to surface” without reason.
👉 Always mention Gauss’s law.

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4. Electrostatic potential is constant throughout the conductor

Why?

Relation between electric field and potential for a conductor

In electrostatic equilibrium, the electric field inside a conductor is zero.

Consider two very close points A and B inside a conductor, separated by a small distance dl.

The work done W in moving a unit positive test charge from A to B is given by:

$$W=E\times dl$$

But inside a conductor:

$$E=0$$

So,

$$W=0$$

Now, electrostatic potential difference is defined as:

$$V_A-V_B=\text{work done per unit charge}$$

Since work done is zero,

$$V_A-V_B=0$$

This gives:

$$\boxed{{\displaystyle V_A=V_B}}$$

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Conclusion (for conductor only)

• The electric field inside a conductor is zero

• Therefore, no work is done in moving a charge inside the conductor

• Hence, electrostatic potential remains the same at all points inside the conductor

$$\boxed{{\displaystyle \text{Electrostatic potential is constant throughout the conductor}}}$$

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5. Electric field just outside the surface of a charged conductor

Derivation idea (pillbox Gaussian surface):

• Take a small cylindrical Gaussian surface (pillbox)

• One face inside (where $E=0$)

• One face outside (where $E\mathrm{\ne }0$)

Using Gauss’s law:

$$EdS=\frac{\sigma dS}{{\epsilon }_0}$$

Result:

$$\boxed{{\displaystyle E=\frac{\sigma }{{\epsilon }_0}}}$$

where:

• $\sigma$ = surface charge density

Direction:

• For positive charge → outward

• For negative charge → inward

📌 Very frequently asked formula

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6. Electrostatic shielding (Cavity inside a conductor)

Statement:

• If a conductor has a cavity

• And no charge is inside the cavity

• Then electric field inside the cavity is zero

Why does this happen?

• Charges reside only on the outer surface

• External fields rearrange charges on outer surface

• The field inside cancels completely

Result:

$$\boxed{{\displaystyle E_{\text{cavity}}=0}}$$

Applications:

• Faraday cage

• Shielding of electronic instruments

• Coaxial cables

• Lightning protection

📌 Exam line:

“A cavity inside a conductor remains completely shielded from external electrostatic fields.”

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Final One-Page Summary (Revise before exam)

• Electric field inside conductor = 0

• Excess charge lies only on surface

• Field at surface is normal

• Potential is constant throughout conductor

• Just outside surface: $E=\sigma \mathrm{/}{\epsilon }_0$

• Cavity inside conductor is electrostatically shielded