Electric Charges - Class 12 Jharkhand Board Physics

Electric Charges and Fields

Introduction to Electricity and Types of Electricity

Electricity refers to the phenomenon of electric charge, commonly experienced as "bijli" or the flow of current in wires. There are two main types of electricity: static electricity (when charge is at rest) and current electricity (when charge is in motion). Static electricity involves charges that remain stationary, while current electricity involves moving charges.

• Static Electricity: Charge at rest; also called electrostatics.
• Current Electricity: Charge in motion; will be studied in later chapters.

Electric Charge: Definition and Nature

Electric charge is a fundamental property…

Electric Charges and Fields

Introduction to Electricity and Types of Electricity

Electricity refers to the phenomenon of electric charge, commonly experienced as "bijli" or the flow of current in wires. There are two main types of electricity: static electricity (when charge is at rest) and current electricity (when charge is in motion). Static electricity involves charges that remain stationary, while current electricity involves moving charges.

• Static Electricity: Charge at rest; also called electrostatics.
• Current Electricity: Charge in motion; will be studied in later chapters.

Electric Charge: Definition and Nature

Electric charge is a fundamental property of matter that causes it to experience a force when placed near another charged object. Only charged bodies can attract or repel each other, while neutral (uncharged) bodies do not interact in this way.

• Definition: Electric charge is the property of matter responsible for electric forces between objects.
• Representation: Charge is denoted by $q$.
• Types: There are two types of charges—positive ($+q$) and negative ($-q$).

Properties of Electric Charge

Electric charge exhibits several key properties, including additivity, quantization, conservation, invariance, and its scalar nature. These properties govern how charges interact and behave in different situations.

• Additivity: The total charge on a body is the algebraic sum of all individual charges present.
• Quantization: Charge exists in discrete packets; the charge on a body is always an integer multiple of the elementary charge ($e$).
• Conservation: Charge can neither be created nor destroyed, only transferred.
• Invariance: The value of charge does not change with location or motion, unlike mass.
• Scalar Quantity: Charge does not depend on direction.

Structure of Atom and Distribution of Charge

All matter is made up of atoms, which consist of a nucleus (containing protons and neutrons) and electrons revolving around the nucleus. The distribution of charge within the atom determines its overall neutrality or charge.

• Proton: Located in the nucleus, carries positive charge.
• Neutron: Located in the nucleus, carries zero charge.
• Electron: Revolves around the nucleus, carries negative charge.
• Neutral Atom: Number of protons equals number of electrons; net charge is zero.
• Charged Atom (Ion): If electrons are lost, atom becomes positively charged (cation); if electrons are gained, atom becomes negatively charged (anion).

Quantization of Charge

Charge is always found in integral multiples of the elementary charge ($e$). The quantization rule is expressed as $q = \pm n e$, where $n$ is an integer and $e$ is the charge of a single electron.

• Elementary Charge: $e = 1.6 \times 10^{-19}$ C (for both electron and proton, but with opposite signs).
• Quantization Formula: $q = \pm n e$
• Possible Values: Only integer multiples of $e$ are possible; fractional charges do not exist in isolation.
• Examples:
  • If $q = 1.6 \times 10^{-18}$ C, $n = 10$ (possible).
  • If $q = 3.2 \times 10^{-20}$ C, $n = 0.2$ (not possible).

Methods of Charging a Body

A neutral body can be charged by transferring electrons using different methods. The main methods are conduction, friction, and induction.

• Conduction: Charging by direct contact; electrons transfer from one body to another when touched.
• Friction: Charging by rubbing two bodies together; the weaker material loses electrons and becomes positive, the stronger gains electrons and becomes negative.
• Induction: Charging without contact; a charged body brought near a neutral conductor causes redistribution of charges, and grounding allows one type of charge to leave, leaving the body charged.

Coulomb’s Law: Force Between Two Point Charges

Coulomb’s Law quantifies the force between two point charges. The force depends on the product of the charges and inversely on the square of the distance between them.

• Statement: The force between two point charges $q_1$ and $q_2$ separated by distance $r$ is$$F = k \frac{q_1 q_2}{r^2}$$
• $k$ (Electrostatic Constant): For air, $k = 9 \times 10^9$ (as stated).
• Nature of Force:
  • Like charges repel, unlike charges attract.
  • The force acts along the line joining the charges.
  • The force is central (acts along the center).
• Units: $F$ in newtons (N), $q$ in coulombs (C), $r$ in meters (m).
• Direction: Use vector notation; for rightward force, use $\hat{i}$, for leftward $-\hat{i}$, etc.

Superposition Principle and Net Force Calculation

When multiple charges are present, the net force on a charge is the vector sum of forces due to all other charges. For symmetric arrangements, forces may cancel.

• Example: Four equal charges at the corners of a square exert zero net force at the center due to symmetry.
• Vector Addition: For two forces $F_1$ and $F_2$ at angle $\theta$,$$F_{net} = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos \theta}$$
• Equilateral Triangle Example: If two forces $F$ and $2F$ act at $60^\circ$, net force is $F_{net} = \sqrt{F^2 + (2F)^2 + 2F \cdot 2F \cdot \cos 60^\circ}$.

Equilibrium of Charges and Positioning

A charge is in equilibrium if the net force on it is zero. The position of equilibrium depends on the nature and magnitude of surrounding charges.

• For unlike charges (e.g., $+q$ and $-10q$): Equilibrium position is outside, near the smaller charge.
• For like charges (e.g., $+q$ and $+10q$): Equilibrium position is between the charges, closer to the smaller charge.
• Rule: Never place a test charge between a positive and negative charge (couple); equilibrium is not possible there.

Sample Problems and Applications

Several types of problems can be constructed using the above principles, including finding net force, equilibrium positions, and charge quantization.

• Quantization Check: To check if a charge value is possible, divide the given charge by $e$; if the result is an integer, it is possible.
• Force Calculation: Use Coulomb’s Law for each pair and vector addition for net force.
• Equilibrium Condition: Set the sum of forces to zero and solve for the required position or value.

Key Exam Takeaways

• Charge is always quantized and conserved.
• Coulomb’s Law applies to point charges at rest.
• Like charges repel, unlike charges attract.
• Net force is found by vector addition of all individual forces.
• Equilibrium positions depend on the relative magnitudes and signs of charges.
• Charge cannot exist without mass, but mass can exist without charge.
• Charge is a scalar quantity and does not depend on direction.
• Methods of charging: conduction (touch), friction (rubbing), induction (without contact).
• For equilibrium, net force on the charge must be zero.