Physics and Mathematics
Electric Charge
1. Statement of the Concept (Electric Charge)
Electric charge is a fundamental property of matter that causes it to experience electrical forces. Bodies can have positive, negative, or zero (neutral) charge, and charged bodies interact according to Coulomb’s law.
2. Clear Explanation and Mathematical Derivation
What is Electric Charge?
Electric charge is an intrinsic property of elementary particles (like electrons and protons) due to which they exert electric forces on each other.
- Proton → +e
- Electron → −e
- Neutron → 0
The smallest possible free charge is the charge of an electron or proton, whose magnitude is:
[ e = 1.6 \times 10^{-19} \text{ C} ]
Quantization of Charge
Charge is not continuous; it exists in multiples of e.
[ q = \pm n e ]
Where:
- [ n ] is any integer
- [ e ] is elementary charge
Conservation of Charge
Charge can neither be created nor destroyed. It can only be transferred.
Example: During friction, electrons move from one body to another, but the total charge remains constant.
Additivity of Charge
If a system contains multiple particles with charges [ q_1, q_2, q_3, … ], total charge is:
[ Q_{\text{total}} = \sum q_i ]
Types of Charge Interaction
- Like charges repel
- Unlike charges attract
This is a fundamental law known since Coulomb’s experiments.
3. Dimensions and Units
| Quantity | Unit | Symbol | Dimension |
|---|---|---|---|
| Charge | Coulomb | C | [I T] |
Electric charge is expressed in Coulombs (C) in the SI system.
4. Key Features of Electric Charge
- Electric charge is quantized ([ q = n e ])
- It is conserved in all physical processes
- Charge can be positive, negative, or zero
- Like charges repel, unlike charges attract
- Charge is additive
- Charge is a scalar quantity (no direction)
- Charge on a body depends on excess or deficit of electrons, not protons
5. Important Formulas to Remember
| Concept | Formula |
|---|---|
| Quantization of charge | [ q = \pm n e ] |
| Elementary charge | [ e = 1.6 \times 10^{-19} \text{ C} ] |
| Total charge | [ Q = \sum q_i ] |
| Charge density (surface) | [ \sigma = \dfrac{Q}{A} ] |
| Charge density (volume) | [ \rho = \dfrac{Q}{V} ] |
6. Conceptual Questions with Solutions
1. Why is electric charge quantized?
Because charge always exists in integral multiples of elementary charge: [q = ne]. No experiment has observed a fraction of [e] on an isolated particle.
2. Can a body have a charge of [2.3e]?
No. Since charge must be an integer multiple of [e], [2.3e] is not possible.
3. Why does a glass rod rubbed with silk become positively charged?
Electrons transfer from the glass rod to the silk cloth. Loss of electrons leaves the rod with net positive charge.
4. Why is electric charge always conserved?
Because electrons are transferred between bodies, but they are never created or destroyed in any physical process.
5. If a body has 10 extra electrons, what is its charge?
The charge is: [q = -10e = -10(1.6 \times 10^{-19}) = -1.6 \times 10^{-18} \text{ C}].
6. Is electric charge a scalar or a vector quantity?
Charge is a **scalar** because it has magnitude only and no direction.
7. Why can’t protons move during charging of a solid?
Protons are bound tightly within the nucleus by strong nuclear forces, so only electrons can move.
8. Can a neutral body attract a charged body?
Yes. Due to **electrostatic induction**, charges rearrange inside the neutral object, causing attraction.
9. When two charged bodies touch, does total charge change?
No. The charge redistributes, but the **total charge remains conserved**.
10. What is meant by additivity of charge?
Total charge of a system is the algebraic sum of individual charges: [Q = \sum q_i].
11. Can the net charge of a body be zero?
Yes. A body with equal amounts of positive and negative charges becomes neutral.
12. Does mass of a body change when it is charged?
Yes, slightly. Adding electrons increases mass; removing electrons decreases mass.
13. Why is 1 Coulomb considered a very large unit?
Because [1 \text{ C}] equals [6.25 \times 10^{18}] electron charges, which is extremely large.
14. If charge is quantized, how can it appear continuous?
On a macroscopic scale, the number of charges is extremely large, so the distribution appears continuous.
15. Does electric charge depend on the speed of the object?
No. Charge is an intrinsic property of matter and remains unchanged with motion.
7. FAQ / Common Misconceptions
1. “Positive charge means protons are added.”
No. Positive charge means **electrons are removed**, not protons added.
2. “Neutral objects have no charges.”
No. They contain equal numbers of positive and negative charges.
3. “Only charged bodies experience electric forces.”
False. A charged object can attract a neutral object through induction.
4. “Charge can be created during friction.”
Incorrect. Friction only **transfers** electrons; total charge remains conserved.
5. “Electric current in solids is due to movement of protons.”
No. Only electrons move; protons are bound inside the nucleus.
6. “Quantization implies charge is always small.”
Large bodies can have huge charge, but still in multiples of [e].
7. “A charged body must have excess protons.”
No. A positively charged body has **fewer electrons**, not more protons.
8. “Charge exists without matter.”
Impossible. Charge is a property of matter; it cannot exist independently.
9. “All charged objects are dangerous.”
No. Only objects with large charge or high potential difference are hazardous.
10. “Electric force acts only in contact.”
No. Electric force is a **non-contact** force that acts at a distance.
8. Practice Questions (with Step-by-Step Solutions)
1. How many electrons are present in 1 C of charge?
[ n = \dfrac{Q}{e}] [= \dfrac{1}{1.6 \times 10^{-19}}] [= 6.25 \times 10^{18} ]
2. A body has a charge of [ -3.2 \times 10^{-19} \text{ C} ]. How many extra electrons does it have?
[ n] = \dfrac{3.2 \times 10^{-19}}{1.6 \times 10^{-19}}] [= 2 ]
3. A body has 5 × 10⁶ excess electrons. What is its charge?
[ q = -n e] [= -5 \times 10^{6} \times 1.6 \times 10^{-19} ]
[ q = -8 \times 10^{-13} \text{ C} ]
4. Can a body have a charge of [4.8 \times 10^{-19} \text{ C}]?
Check if divisible by [e]:
[ \dfrac{4.8 \times 10^{-19}}{1.6 \times 10^{-19}}] [= 3 ]
Yes, possible.
5. If 10¹⁰ electrons are removed from a neutral body, what is the resulting charge?
[ q = +n e] [= 10^{10} \times 1.6 \times 10^{-19} ]
[ q = 1.6 \times 10^{-9} \text{ C} ]
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