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Electric Charges and Fields Set-1

March 23, 2026

Electric Charges and Fields Set-1 📘

Did you know? Every time you comb your dry hair and it starts attracting tiny bits of paper, you’re actually doing a mini-physics experiment on electric charges and fields. The same ideas explain lightning, photocopiers, touchscreens, and even how your TV works!

Why Electric Charges and Fields Feel So Fundamental ⚡

Electricity is one of the core pillars of modern physics. Class 12 CBSE (and exams like JEE Main, JEE Advanced and NEET) start electromagnetism with this chapter because:

  • It introduces the idea of charge, the most basic “ownership” of electric property.
  • It builds the concept of an electric field, a powerful way to “see” invisible forces.
  • It sets up tools like Coulomb’s law and superposition, which you’ll use again and again in later topics like electric potential, capacitors and current electricity.

If you understand this chapter conceptually, many later topics become much easier. If you skip the concepts and just mug up formulas, almost every tricky question will feel confusing.

Building the Idea of Electric Charge 🧲 (But Make It Electric!)

In physics, electric charge is a fundamental property of matter that causes it to experience electric forces.

Key points to lock in:

  • There are two types of charges: positive and negative.
  • Like charges repel, unlike charges attract.
  • Charge is quantized: the smallest unit of free charge is the charge on an electron or proton, denoted by e.
  • Charge is conserved: in an isolated system, the total charge never changes.

Outside of HTML (for LaTeX):

e=1.6×10−19 Ce = 1.6 \times 10^{-19}\,\text{C}

Quick concept table 🧾

ConceptWhat it means in simple wordsExam angle (CBSE/JEE/NEET)
QuantizationCharge comes in steps of e, not in arbitrary valuesShort answer, reasoning questions
ConservationTotal charge stays constant in an isolated systemFrequently in numerical + MCQs
Additivity of chargeTotal charge is algebraic sum of individual chargesUsed in superposition, field calculations
Scalar vs vectorCharge is scalar, force and field are vectorsDirection mistakes are very common

Conductors, Insulators and Charging Methods 🧪

Real-life objects don’t always allow charges to move freely.

  • Conductors: Have free electrons (like metals). Charges can move throughout the material.
  • Insulators: Electrons are tightly bound. Charges cannot move freely (like rubber, glass, plastic).
  • Semiconductors: In between; important in electronics (silicon, germanium).

How can we charge a body?

  1. By friction (rubbing)

    • Example: Rubbing a balloon on your hair.
    • Electrons are transferred from one material to another.

  2. By conduction (contact)

    • A charged body touches a neutral conductor.
    • Some charge flows until both reach the same potential.

  3. By induction (no contact!)

    • A charged body is brought near a neutral conductor but does not touch it.
    • Charges in the conductor rearrange due to the electric field.
    • If you then connect the conductor to earth and remove the connection and source charge, the conductor is left with net charge.
Exam Tip (CBSE + JEE)
Be clear about which process involves physical contact and which does not. Many conceptual questions simply twist this idea:
  • Friction and conduction: contact.
  • Induction: no contact, but uses grounding/earthing.

Coulomb’s Law: The Gravitational Law of Electrostatics 🌍⚡

Coulomb’s law gives the magnitude of electrostatic force between two point charges in vacuum or air.

Outside of HTML:

F=kq1q2r2F = k \frac{q_1 q_2}{r^2}

Where:

  • FF is the magnitude of force,
  • q1q_1 and q2q_2 are the charges,
  • rr is the distance between them,
  • kk is Coulomb’s constant, given by
k=14πε0k = \frac{1}{4\pi \varepsilon_0}

and

ε0=8.854×10−12 C2N−1m−2\varepsilon_0 = 8.854 \times 10^{-12}\,\text{C}^2\text{N}^{-1}\text{m}^{-2}

Key features you must remember

  • Force acts along the line joining the two charges (it’s central).
  • Force is attractive if signs are opposite, repulsive if signs are same.
  • It obeys inverse square law: if distance doubles, force becomes one-fourth.

Worked Example 1: Coulomb’s Law in Action 🧮

Question:
Two charges 3 µC and –2 µC are separated by 0.3 m in air. Find the magnitude of force between them. Is it attractive or repulsive? (Take k = 9 × 10⁹ N m² C⁻²)

Step 1: Convert to SI units

Outside of HTML:

q1=3 μC=3×10−6 Cq_1 = 3\ \mu\text{C} = 3 \times 10^{-6}\,\text{C} q2=−2 μC=−2×10−6 Cq_2 = -2\ \mu\text{C} = -2 \times 10^{-6}\,\text{C} r=0.3 mr = 0.3\,\text{m}

Step 2: Use Coulomb’s law

Outside of HTML:

F=k∣q1q2∣r2F = k \frac{|q_1 q_2|}{r^2}

Substitute:

F=9×109×(3×10−6)(2×10−6)(0.3)2F = 9 \times 10^9 \times \frac{(3 \times 10^{-6})(2 \times 10^{-6})}{(0.3)^2}

Compute numerator:

(3×10−6)(2×10−6)=6×10−12(3 \times 10^{-6})(2 \times 10^{-6}) = 6 \times 10^{-12}

So,

F=9×109×6×10−120.09F = 9 \times 10^9 \times \frac{6 \times 10^{-12}}{0.09}

Now simplify:

6×10−120.09=60.09×10−12=66.67×10−12\frac{6 \times 10^{-12}}{0.09} = \frac{6}{0.09} \times 10^{-12} = 66.67 \times 10^{-12}

Then:

F≈9×109×66.67×10−12=600×10−3=0.6 NF \approx 9 \times 10^9 \times 66.67 \times 10^{-12} = 600 \times 10^{-3} = 0.6\,\text{N}

Step 3: Direction of force

  • Signs are opposite (3 µC and –2 µC), so force is attractive.

Answer:
Magnitude of force is approximately 0.6 N and it is attractive.

Principle of Superposition: Many Charges at Once 🎯

Real problems rarely have just two charges. The superposition principle allows you to calculate the net force on any charge due to multiple other charges.

  • Force due to each charge is calculated independently as if the others don’t exist.
  • Then you add all those force vectors vectorially (taking direction into account).
Common Mistake Alert
Students often add forces algebraically even when they are not along the same line. Remember:
  • Use algebraic sum only if all forces lie on the same straight line.
  • Otherwise resolve into components (usually along x and y) and then add.

Electric Field: Force Spread Out in Space 🌌

Imagine placing a tiny positive test charge near a source charge. It experiences a force. Instead of saying “the charge exerts a force only on that particle”, physicists say “the charge creates an electric field in space”.

Definition:
Electric field at a point is the force per unit positive test charge placed at that point.

Outside of HTML:

E⃗=F⃗q\vec{E} = \frac{\vec{F}}{q}

For a point charge Q, the electric field at distance r is:

E=kQr2E = k \frac{Q}{r^2}
  • Direction: away from Q if Q is positive, towards Q if Q is negative.

Why electric field is a powerful idea (especially for JEE/NEET)

  • You can separate “source” (which creates field) from “test charge” (which experiences force).
  • You can find field at various points first, then get force on any charge simply using F = qE.
  • This is crucial for continuous charge distributions (lines, rings, surfaces) and is heavily tested in competitive exams.

Visualising Electric Field Lines 🎨

Since we can’t see fields, we draw field lines.

Rules of field lines (very exam-friendly)

  • They start from positive charges and end on negative charges.
  • They never intersect (because that would mean two directions of field at the same point).
  • The density of lines represents the strength of the field.
  • For an isolated positive charge: lines radiate outward symmetrically in all directions.
  • For an isolated negative charge: lines converge inward.

Diagram description (for your notebook)

  • Draw a positive point charge at the centre of the page.
  • Draw straight arrows going outward equally spaced in all directions (like a sun).
  • Label them as “electric field lines of a positive point charge”.

Then:

  • Draw a negative point charge.
  • Draw arrows directed towards it from all directions.
  • Label them as “electric field lines of a negative point charge”.

Electric Dipole: Two Opposite Charges, Small Distance Apart 🧲⚡

An electric dipole is a pair of equal and opposite point charges separated by a small distance.

If the charges are +q and –q and the separation is 2a, the dipole moment p is defined as:

Outside of HTML:

p⃗=q×2a⃗\vec{p} = q \times 2\vec{a}

Direction of dipole moment: from negative charge to positive charge.

Why dipoles matter:

  • Many molecules (like HCl, H₂O) behave like electric dipoles.
  • Fields of dipoles are important both in Class 12 and in advanced exams like JEE.

Worked Example 2: Electric Field Near a Point Charge 🧮

Question:
A point charge of 5 nC is placed in air. Find the magnitude of electric field at a point 0.2 m away from it. (Take k = 9 × 10⁹ N m² C⁻²)

Step 1: Convert to SI

Outside of HTML:

Q=5 nC=5×10−9 CQ = 5\,\text{nC} = 5 \times 10^{-9}\,\text{C} r=0.2 mr = 0.2\,\text{m}

Step 2: Use the formula

Outside of HTML:

E=kQr2E = k \frac{Q}{r^2}

Substitute values:

E=9×109×5×10−9(0.2)2E = 9 \times 10^9 \times \frac{5 \times 10^{-9}}{(0.2)^2}

Compute denominator:

(0.2)2=0.04(0.2)^2 = 0.04

So:

E=9×109×5×10−90.04=9×109×125×10−9E = 9 \times 10^9 \times \frac{5 \times 10^{-9}}{0.04} = 9 \times 10^9 \times 125 \times 10^{-9}

Now:

9×125=11259 \times 125 = 1125

So:

E=1125 N C−1E = 1125\ \text{N C}^{-1}

Answer:
Electric field at the point is 1125 N C⁻¹, directed radially outward (since the charge is positive).

Real-Life Connections: Where You’ve Already Met These Ideas 🌩️📱

  • Lightning: Enormous electric fields build up between clouds and ground due to charge separation. When field strength exceeds air’s breakdown limit, a discharge (lightning) occurs.
  • Photocopiers and laser printers: Use charged drums and electric fields to attract toner particles to specific regions.
  • Capacitive touchscreens: Your finger slightly changes the local electric field distribution, which is detected by the device.
  • Molecules in biology: Many interactions between biomolecules are governed by electric forces and fields arising from charges and dipoles.

Connecting these physical ideas to real devices will help you write better answers in theory questions (especially for CBSE board exams, where explanations and diagrams are crucial).

Snapshot Revision: Key Formulas from This Set-1 🧠📋

  • Coulomb’s law (force between two point charges)

Outside of HTML:

F=kq1q2r2F = k \frac{q_1 q_2}{r^2}
  • Coulomb’s constant in vacuum
k=14πε0k = \frac{1}{4\pi \varepsilon_0}
  • Electric field definition
E⃗=F⃗q\vec{E} = \frac{\vec{F}}{q}
  • Electric field due to a point charge
E=kQr2E = k \frac{Q}{r^2}

  • Direction rules

    • Positive source charge: field radially outward.
    • Negative source charge: field radially inward.

  • Qualitative ideas

    • Electric field is a vector.
    • Charge is scalar, but can be positive or negative.
    • Principle of superposition applies to both forces and fields.

High-Value Exam Traps and How to Avoid Them 🚫🎓

  1. Confusing sign of charge with direction of force/field

    • Sign of charge does not make field negative; it just changes direction.
    • Always think: “What would a positive test charge do here?”

  2. Forgetting units

    • Charge: coulomb (C)
    • Electric field: newton per coulomb (N C⁻¹)
    • Force: newton (N)
      Dimension and unit-based MCQs are easy marks—don’t lose them.

  3. Treating extended bodies as point charges without checking conditions

    • Coulomb’s law strictly holds for point charges.
    • For charged spheres, you can treat the whole charge as concentrated at the centre only if you are outside the sphere and it is a conductor (or spherically symmetric distribution).

  4. Not drawing diagrams

    • For questions involving field lines, dipoles or multiple charges, a neat diagram often reveals the answer faster than long algebra.
Strategy Tip for Competitive Exams
  • Memorise only a few core formulas: Coulomb’s law, field of a point charge, superposition.
  • Spend more effort on understanding patterns: symmetry, cancellation of fields, and direction of forces.
  • Practice mixed conceptual + numerical problems, since JEE/NEET often test both in a single question.

How to Practise This Chapter Smartly 🧭

  • Start with simple two-charge numericals to fix ideas of Coulomb’s law.
  • Move to three-charge systems to apply superposition.
  • Draw field line diagrams for single charges, pairs of charges, and dipoles.
  • Revise definitions and units quickly every day; they often appear in 1-mark questions in CBSE and as direct MCQs in JEE/NEET.

Ready to Test Yourself? 📝

Put your understanding of:

  • charge and its properties,
  • Coulomb’s law,
  • superposition principle, and
  • basic electric field concepts

to the test with a focused question set designed for Class 12 and competitive exams.

👉 Start practising “Electric Charges and Fields” now

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Electric Charges and Fields Set-1