Electric Charge

q  –  Electric Charge

Electric charge is a fundamental property of matter that produces electric forces. It exists in two kinds—positive and negative. Charge is quantized in units of \(e = 1.6 \times 10^{-19}\,\text{C}\). The total charge of an isolated system is always conserved.

Electric Field

Electric Field (E)

The electric field is the space around a charge where another charge feels an electric force. Its direction is the force on a +1 C test charge.

Key Characteristics:

  • Vector quantity; magnitude \(E = F / q\); arrows show size and direction.
  • Field lines emerge from positive charges and terminate on negatives, never crossing.
  • Line density depicts field strength; closer lines indicate a stronger field.
  • Tangent to a field line gives the local direction of \(\mathbf{E}\).

Example:

Radial arrows spreading outward from an isolated +q illustrate its electric field pattern.

Coulomb’s Law

\[F = k \dfrac{q_1 q_2}{r^2}\]

Variable Definitions

k Coulomb constant, \(1/(4\pi\varepsilon_0)\)
\(q_1\) first point charge
\(q_2\) second point charge
r distance between charges
\( \varepsilon_0 \) vacuum permittivity

Applications

Atomic Scale

Find repulsive force between two electrons 0.1 nm apart.

Macroscopic Charges

Estimate attraction between a charged rod and metal sphere in air.

Source: NCERT Physics Class 11

Electric vs Magnetic Fields

Electric Field

Produced by static or moving electric charge.
Lines start on +, end on −; never close.
Force \( \mathbf{F}=q\mathbf{E} \) acts on any charge.

Magnetic Field

Produced by moving charge, currents or magnetic moments.
Lines form closed loops; encircle current via right-hand rule.
Force \( \mathbf{F}=q\mathbf{v}\times\mathbf{B} \) on moving charges or currents.

Key Similarities

Both are vector fields filling space.
Both obey superposition; fields add linearly.
Both store energy and form electromagnetic waves.

Moving Charges Produce Magnetic Fields

Photograph of compass needles forming concentric circles around a vertical current-carrying wire

Compass needles trace circular magnetic field lines around a current-carrying wire.

From Ørsted’s spark to the right-hand rule

Ørsted showed a compass deflects near a live wire, proving a current creates a magnetic field.

This field forms concentric circles around the conductor in planes perpendicular to the current.

Key Points:

  • Field lines are closed, circular loops centred on the wire.
  • Right-hand rule: thumb = current; curled fingers = magnetic field direction.
  • Greater current strengthens the field; circles crowd near the wire.

Faraday’s Law of Induction

\(\varepsilon = -\dfrac{d\Phi_B}{dt}\)

Variable Definitions

\( \varepsilon \) Induced emf (V)
\( \Phi_B \) Magnetic flux (Wb)
\( t \) Time (s)
\( - \) Opposes change (Lenz’s law)

Applications

Generators

Rotating coils cut magnetic flux to create electricity in power stations.

Transformers

A changing primary flux induces a different voltage in the secondary coil.

Induction Cooktops

Rapidly varying fields induce currents that heat the pan directly.

How Electromagnetic Induction Works

Induction starts with motion and ends with current. Sequence each stage to understand the process.

1

Relative Motion

Move the magnet and coil toward or away from each other, or slide the coil through the field.

2

Flux Change

Motion alters the magnetic flux Φ threading the coil’s loops.

3

Induced emf

A changing Φ produces emf: \( \mathcal{E} = -\\dfrac{d\\Phi}{dt} \).

4

Current Direction by Lenz

The induced current flows so its own field opposes the original flux change.

Pro Tip:

No flux change → no emf. Keep something moving to generate current.

Multiple Choice Question

Question

A bar magnet enters a coil and produces an emf of 2 V. If its speed is doubled, what is the new emf magnitude?

1
Remains 2 V
2
Becomes 1 V
3
Becomes 4 V
4
Drops to 0 V

Hint:

Faraday’s law: emf is proportional to the rate of change of magnetic flux.

Key Takeaways

Electric charge sets up an electric field that pushes or pulls other charges.

Coulomb’s law: \(F = k \\frac{q_1q_2}{r^2}\) acts along the line joining two point charges.

A steady current produces a magnetic field that circles the conductor.

Faraday’s law: changing magnetic flux induces emf \(\\varepsilon = -\\frac{d\\Phi_B}{dt}\).

Together, these laws reveal electricity and magnetism as two facets of electromagnetism.

Thank You!

We hope you found this lesson informative and engaging.