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CBSE Class 12 · Physics

Electric Charges and Fields

Official NCERT chapter from Physics Part I–II (book code leph1). ExamMaster notes are original teaching at CBSE Class 12 depth.

This lesson follows the official chapter “Electric Charges and Fields” in Physics Part I–II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 12
  • Medium level
  • 12 concepts

1Electric Charge

Electric charge is the school source of electric push and pull as taught — plus or minus. Charge is a property with a unit (coulomb). Like signs push; unlike pull. A charge is not a current (that is moving charge later).

A magnet-pole labelled charge because both “attract” is a miss.

Figure. Unlike charges attract along the line joining them. The two arrows are the pair of forces: equal length, opposite direction. Like charges would both arrows reverse. Lengths here are schematic, not a newton scale.

How it works

  1. Name plus or minus and the coulombCharge.
  2. State like-push, unlike-pullThe look.
  3. Keep current as a later wordThis heading.

2Conductors and Insulators

Conductors let charge move through as taught; insulators hold it. A metal is the school conductor; dry rubber an insulator. The split is a move-or-hold test, not “shiny”.

Calling every solid an insulator is a steal.

Figure. On a conductor the extra charge sits on the outer rim — the interior of the metal box is empty. On an insulator the same extra charge stays where it was placed. The boxes are topology, not a micrograph of atoms.

How it works

  1. Ask whether charge can move throughThe test.
  2. Name conductor or insulatorThe word.
  3. Refuse shiny as the testA move-look.

3Basic Properties of Electric Charge

Basic properties: additivity, conservation, quantisation as taught. Charge adds; a closed system keeps the total; e is the school quantum if named. Properties are three tests, not a biography.

Creating + without − in a closed pair is a conservation-miss.

Figure. Charge comes in whole steps of e. A bar of 2e is twice 1e; there is no bar of 1.5e. Conservation is a later sentence: these three bars are the quantization claim only.

How it works

  1. Name add, conserve, or quantum-eThe property.
  2. Run it on a pair of objectsThe test.
  3. Keep e as the taught bit if askedHonest.

4Coulomb’s Law

Coulomb’s law: F = k q1 q2 / r^2 along the join as taught. Two point charges; k as the school factor. 2 μC and 3 μC a metre apart is a size-story if computed. Coulomb is an inverse-square pair, not a field yet.

Using r instead of r^2 is a miss.

Figure. Coulomb: F = k q1 q2 / r². Two +3 μC charges 20 cm apart give F = 9×10⁹ × (3×10⁻⁶)² / 0.04 = 2.025 N. The arrows are equal and point away — like charges repel. Lengths are schematic; the number on each arrow is the force.

How it works

  1. Copy q1, q2, rThe given.
  2. Form k q1 q2 / r^2The force.
  3. Keep the along-the-join directionPush or pull.

Coulomb size

q1=2e-6 C, q2=3e-6 C, r=1 m, k=9e9. Find F.

  • q1 q26e-12
  • k q1 q2 / r^29e9 × 6e-12 = 0.054 N
  • Readalong the join

Pro tip. Inverse square; r=1 keeps the write short.

5Forces between Multiple Charges

Multiple charges: the net force is the vector sum of pair-Coulombs as taught. Superposition is add-the-vectors, not add-the-numbers if directions differ. Three charges need two pair-arrows at the one you watch.

Adding 0.054 and 0.054 as 0.108 when they oppose is a miss.

Figure. Superposition on the middle +1 μC. The 2 μC pushes 0.80 N right; the 4 μC pushes 1.60 N left. Those two arrows are drawn 1 : 2. The leftover 0.80 N points toward the weaker charge. A charge sitting between does not screen the pair.

How it works

  1. Draw each pair-force on the charge you watchThe arrows.
  2. Add as vectorsThe net.
  3. Keep superposition as the nameThe rule.

6Electric Field

Electric field: force per unit test charge, E=F/q as taught. A field is a map of arrows, not a second charge. Point-charge E = k q / r^2. Field is what a later charge would feel.

Using F as E without dividing by q is a miss.

Figure. This is the field sampled at points, not drawn as continuous lines. Four inner arrows sit at one radius and are 0.12 tall in visual units. Four outer arrows sit at twice that radius and are 0.03 tall — a quarter as long, the inverse square made visible. Continuous field lines would crowd the same information.

How it works

  1. Name F on a small q, then E=F/qThe field.
  2. Keep the unit N/C (or V/m later)The label.
  3. Refuse a field as a blob of chargeA map.

7Electric Field Lines

Field lines: start on plus, end on minus as taught; density hints strength; they do not cross. A line is a map-mark, not a rope. One plus-to-minus sketch is enough.

Two lines crossing as “stronger” is a miss.

Figure. Field-line topology without drawing curves: arrows begin on plus and end on minus, and they do not cross. These are straight samples along three paths, not a crowding picture. Magnitude still lives in the inverse-square sample of the previous figure.

How it works

  1. Draw plus to minus, no crossThe lines.
  2. Read crowding as strongerThe hint.
  3. Keep it a map, not a wireHonest.

8Electric Flux

Electric flux: E times area with the taught cosine (E·A). Flux through a closed surface later feeds Gauss. Flux is a through-count, not a flow of water.

Using E×A with no angle when they are not perpendicular is a miss.

Figure. Flux through a flat patch is E times A when E is along the dashed normal. The three E arrows are equal and parallel — a uniform field — and they pierce the rectangle. Tilt the patch and the same arrows count only the part along the normal. The rectangle is the area; there is no shade for the piercing.

How it works

  1. Name E, A, and the angle as taughtThe inputs.
  2. Form E A cosθFlux.
  3. Keep it a through-wordNot a current.

9Electric Dipole

A dipole: +q and −q a small apart as taught; moment p=q×2a along minus-to-plus. Dipole is a pair-with-an-arrow, not a single charge. Field on axis versus equator if taught.

A single + as “a dipole” is a miss.

Figure. A dipole is equal and opposite charges a length 2a apart. The moment p points from minus to plus and has size q times 2a. The arrow is the moment, not a force.

How it works

  1. Name +q and −q separatedThe dipole.
  2. Write p along minus-to-plusThe moment.
  3. Keep it a pairTwo charges.

10Dipole in a Uniform External Field

Dipole in a uniform field: net force 0 as taught; a torque tries to align p with E, τ=p E sinθ. Uniform means the two forces cancel as a couple. A non-uniform field can also pull — if named.

A net force in a uniform field as the first claim is a miss.

Figure. Uniform E is the three parallel arrows. Force on +q is qE along E; force on −q is qE against E. The two qE arrows are drawn the same length. They cancel as a net force and remain as a couple that turns p toward E. Arrow lengths are schematic, not a newton scale.

How it works

  1. Uniform → net F=0, leftover torqueThe look.
  2. Write τ=p E sinθ as taughtThe torque.
  3. Keep align as the jobp with E.

11Continuous Charge Distribution

Continuous charge: a line, surface, or volume density as taught (λ, σ, ρ). Continuous is a smear-instead-of-points. One λ=charge/length is enough to name the idea.

A point-Coulomb dump as the whole continuous heading is a skip.

Figure. A continuous distribution is a density, not a pile of named charges. λ is charge per length on a line, σ per area on a sheet, ρ per volume in a block. The boxes grow in the number of filled dimensions.

How it works

  1. Name λ, σ, or ρ as charge per length/area/volumeThe density.
  2. Integrate or use Gauss later as taughtThe use.
  3. Keep it a smear-wordNot one point.

12Gauss’s Law

Gauss’s law (school): flux through a closed surface equals q_enclosed / ε0 as taught. Gauss is a symmetry-shortcut, not a new Coulomb. A spherical shell’s outside field matches a point as the school use.

Using q_total-on-the-page when charge sits outside the surface is a miss.

Figure. Gauss for a line charge uses a cylinder drawn side-on — a rectangle, so the shape is honest. Flux leaves through the wall (the two vertical sides). The top and bottom lids are parallel to the radial field, so they carry no flux. Enclosed charge is λ times the height. A spherical Gaussian surface is an arc and is not drawn.

How it works

  1. Pick a symmetric closed surfaceThe Gaussian.
  2. Write flux = q_in / ε0The law.
  3. Keep outside-charge off q_inThe caution.
Coulomb’s F tracks
  1. 1/r^2 along the join as taught
  2. r
  3. Only a field line

Inverse square.

Notes

  • Mapped to the official NCERT chapter “Electric Charges and Fields”. Original teaching only — no textbook sentences.
  • Science here is Physics, Chemistry and Biology ideas at this class, never a language or social-science chapter.

Formulas

  • F=k q1 q2 / r^2
  • E=F/q
  • flux = E A cosθ
  • Gauss: flux = q_in / ε0

Recap

Hold these pegs from the official chapter “Electric Charges and Fields”. The wording is ExamMaster’s teaching, not a textbook recap.

Electric Charge
Electric charge is the school source of electric push and pull as taught — plus or minus.
Conductors and Insulators
Conductors let charge move through as taught; insulators hold it.
Basic Properties of Electric Charge
Basic properties: additivity, conservation, quantisation as taught.
Coulomb’s Law
Coulomb’s law: F = k q1 q2 / r^2 along the join as taught.
Forces between Multiple Charges
Multiple charges: the net force is the vector sum of pair-Coulombs as taught.
Electric Field
Electric field: force per unit test charge, E=F/q as taught.

Practise Electric Charges and Fields

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