Electrostatics: Class 10 Physics

Key points

Electrostatics is the study of charges at rest. There are two kinds of charge, positive and negative. Like charges repel and unlike charges attract. When a glass rod is rubbed with silk, electrons move from the rod to the silk, so the rod becomes positive and the silk negative. Only electrons move. The protons stay fixed in the nucleus.

Charge is measured in coulomb (C). The charge of one electron is 1.6 × 10⁻¹⁹ C. Charge is quantized, which means any charge is a whole-number multiple of this value (q = n e). Charge is also conserved: it can be moved from one body to another but never created or destroyed. In practice we use microcoulomb (1 μC = 10⁻⁶ C).

Materials are conductors, which allow charge to flow easily (metals, the human body), or insulators, which do not (rubber, plastic, dry wood, glass). A body can be charged by friction, by contact and by induction. In induction a charged object is brought near, but does not touch, a neutral conductor. Charges in the conductor separate. If the conductor is earthed and then the earth connection is removed before the charged object, the conductor keeps a charge opposite to that of the object.

A gold leaf electroscope detects charge. It has a metal cap, a rod and a thin gold leaf. When a charged body touches the cap, the leaf and the rod gain the same charge and repel each other, so the leaf rises. The bigger the charge, the wider the leaf opens. It can also show the sign of an unknown charge: bringing a charge of the same sign as the electroscope makes the leaf rise further.

Coulomb's law gives the force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them: F = k q₁ q₂ / r². In air k = 9 × 10⁹ N m²/C². It is also written k = 1 / (4π ε₀), where ε₀ = 8.85 × 10⁻¹² C²/(N m²) is the permittivity of free space. Doubling the distance reduces the force to one quarter.

An electric field is the region around a charge where another charge feels a force. The field strength at a point is the force per unit positive test charge: E = F / q. Its unit is N/C (or V/m). For a point charge Q, E = k Q / r². The direction of the field is the direction of the force on a positive charge.

Properties of electric field lines:

• They start from positive charges and end on negative charges.
• They never cross each other.
• Where they are close together the field is strong. Where they are far apart the field is weak.
• In a uniform field, such as between two parallel plates, they are straight, parallel and equally spaced.

Electric potential at a point is the work done in bringing a unit positive charge from infinity to that point. The potential difference between two points is the work done per unit charge in moving a charge from one to the other: V = W / q. Its unit is the volt (V), where 1 V = 1 J/C. In a uniform field E = V / d, where d is the plate separation.

A capacitor stores charge and energy. The simplest type is two parallel metal plates separated by an insulator (dielectric). The capacitance is the charge stored per unit potential difference: C = Q / V. The unit is the farad (F). Because 1 F is very large, we use μF (10⁻⁶ F), nF (10⁻⁹ F) and pF (10⁻¹² F). For parallel plates C = ε₀ A / d in air, so the capacitance grows with plate area and falls with separation. A dielectric between the plates increases the capacitance.

Capacitors in parallel have the same potential difference and their capacitances add: C = C₁ + C₂ + C₃. Capacitors in series have the same charge and the reciprocals add: 1/C = 1/C₁ + 1/C₂ + 1/C₃. Series combinations give a smaller total than the smallest capacitor.

A charged capacitor stores energy: E = ½ C V² = ½ Q V = Q² / (2C). Capacitors are used in camera flash units, tuning circuits in radios, smoothing power supplies, and starting fan and motor circuits. Lightning conductors and earthing protect buildings and equipment from charge build-up.

Study tip: Memorize the value of k and the electron charge, and always convert prefixes to SI before using a formula. For induction questions, draw the three stages (bring the rod, earth the sphere, remove earth then rod) and mark the sign of the charges on each. For capacitors, check your answer by asking whether the series result is smaller and the parallel result larger.

Definitions and flashcards

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Short questions with model answers

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Common mistakes

• Forgetting to square the distance in Coulomb's law, or using centimetres instead of metres.
• Not converting μC to C (1 μC = 10⁻⁶ C) before substituting.
• Adding series capacitors directly. Add the reciprocals instead, and check the result is smaller than the smallest capacitor.
• Drawing field lines that cross, or starting field lines from a negative charge.
• Saying protons move when a body is charged by rubbing. Only electrons move.

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