A spark or crackling sound is often noticed when synthetic clothes or sweaters are removed from the body, especially during dry weather. This often happens with garments made of materials such as polyester sarees. Lightning during thunderstorms is another example of the same phenomenon, electric discharge. A similar small electric shock can also be felt when opening a car door or touching the iron bar of a bus after sliding off the seat.
Induction
These sensations occur due to the discharge of electric charges that accumulate when insulating surfaces rub against each other. This phenomenon is known as static electricity. The term "static" refers to something that does not move or change with time. The branch of physics that studies forces, fields, and potentials produced by stationary charges is called electrostatics.
Most bodies are electrically neutral, meaning they contain equal amounts of positive and negative charges. To charge a neutral body, this balance must be disturbed. The charge balance of a neutral body can be altered by the following methods:
- Friction
- Conduction
- Induction
1. Charging by Friction
The charging by friction method includes rubbing one particle against another, causing electrons to move from one surface to the next. This procedure can be used to charge insulators.
Different materials have different electrical properties because of the types of atoms and their combinations. Electron affinity is the property that describes how strongly a substance attracts electrons. Materials with high electron affinity tend to gain electrons easily. Triboelectric charging (charging by friction) depends on this property. For example, when a rubber balloon is rubbed with animal fur, their atoms come close and their electron clouds interact. Since rubber has a stronger affinity for electrons, it takes electrons from the fur, causing both objects to become charged. Similarly, when glass rods are rubbed with wool or silk cloth, they repel each other, while the glass rod and the cloth attract each other due to opposite charges.
2. Charging by Conduction
Charging by conduction occurs when a charged object comes into direct contact with a neutral conductor, allowing charges to transfer between them. This method is mainly used to charge conductors.
Example: If a positively charged aluminum plate touches a neutral metal sphere, electrons from the sphere move toward the plate, causing the sphere to become positively charged. Similarly, when a negatively charged metal sphere touches the plate of a neutral electroscope, the electroscope becomes charged.
Another example is when a person standing on an insulating platform touches a negatively charged Van de Graaff generator, causing the person to become charged. In conduction charging, the charged and neutral objects must touch each other, which is why it is also called charging by touch.
3. Charging By Induction
Induction charging is a charging method in which a neutral object is charged without actually touching another charged object. The charged particle is held near a neutral or uncharged conductive material that is grounded on a neutrally charged material. When a charge flows between two objects, the uncharged conductive material develops a charge with the polarity opposite that of the charged object.
(1) Charging by induction using a positively charged rod:
Charging by induction using a positively charged rod involves placing two metal spheres, A and B, on insulating platforms and bringing them close together. A positively charged rod is brought near the sphere. A, without touching it, attracting electrons in the spheres. Sphere A develops a negative charge near the rod, while sphere B develops a positive charge on the far side. The charges redistribute until electrostatic equilibrium is reached and remain visible while the rod is nearby. Slightly separating the spheres while keeping the rod close causes them to carry opposite charges and attract each other. Once the rod is removed and the spheres are fully separated, the charges distribute evenly. This method leaves the spheres equal and oppositely charged, and unlike conduction, the rod does not lose any of its charge.
(2) Charging by induction using a negatively charged rod:
Consider two metal spheres, A and B, touching each other. When a negatively charged rod is brought near, the electrons in the spheres repel and move from sphere A to sphere B. As a result, sphere A becomes positively charged and sphere B negatively charged, while the overall system remains electrically neutral. According to the diagram, the spheres are then separated without touching each other, and after removing the rod, the charges redistribute evenly over both spheres, leaving them oppositely charged.
Electrostatic vs. Electromagnetic Induction.
| S. no. | Electromagnetic Induction | Electrostatic Induction |
|---|---|---|
| 1. | Without any electrical connection, the formation of emf in a conductor due to the rate of change of current in a neighboring conductor. | Without any physical contact, the collection or redistribution of electric charges in a body caused by a neighboring charged body. |
| 2. | It is effective across great distances. | It is effective across short distances. |
| 3. | It's because of the rate of change in charge flow. | It's because of static charges. |
| 4. | In conductors, the effect is strongest. | In insulators, the effect is strongest. |
| 5. | The cause for this is due to the electric fields of the charges. | The cause is magnetic fields caused by moving charges. |
Law of Conservation of Charge
Charge is a property of matter that allows it to create and experience electrical and magnetic effects. The law of conservation of charge states that the total charge in an isolated system always remains constant. At any two time intervals, a system that does not exchange mass or energy with its surroundings will have the same total charge. For example, if two objects in an isolated system initially have zero net charge and one transfers one million electrons to the other, the object gaining electrons becomes negatively charged, and the one losing electrons becomes positively charged with the same magnitude. The total charge of the system remains unchanged.
Properties of Electric Charges
Additivity of Charges:
- In a system with two point charges, q1 and q2, the total charge is determined by algebraically adding q1 and q2, similar to how real numbers are added.
- For a system with n charges (q1, q2, q3,...qn), the total charge is calculated as (q1 + q2 + q3...qn).
- Charge, like mass, possesses magnitude but lacks direction.
- Unlike mass, which is always positive, charge can be positive or negative.
- When adding charges to a system, specific conventions must be followed to indicate the sign of each charge.
Quantization of Electric Charge:
Electric charge is quantized, meaning all charges are integer multiples of a basic unit of charge, eee. The charge q on a body is given by.
q = ne
where n is a positive or negative integer. The electron carries a charge of −e, while the proton carries a charge of +e.
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Sample Problems
Question 1: How many electrons must be removed from a neutral body to give it a charge of + 4.8 × 10⁻¹⁹? (Given: charge of one electron e = 1.6 × 10⁻¹⁹ C)
Solution: Number of electrons
n = \frac{q}{e}
n = \frac{4.8 \times 10^{-19}}{1.6 \times 10^{-19}} = 3 3 electrons must be removed.
Question 2: Calculate the total charge on a body that has 8 × 10 excess electrons. (Given: e = 1.6 × 10⁻¹⁹ C)
Solution:
q = n \cdot e
q = (8 \times 10^6) \cdot (-1.6 \times 10^{-19})
= -1.28 \times 10^{-12}\,\text{C}
Question 3: Two charges, q1 = +5 C and q2 = −8 C, are placed in a system. Find the total charge of the system.
Solution:
Q_\text{total} = q_1 + q_2
Q_\text{total} = 5 + (-8) = -3\,\text{C}
Question 4: A neutral metal sphere is placed near a positively charged rod and grounded temporarily. If 1 × 106 electrons flow into the sphere from the ground, find the resulting charge on the sphere.
Solution:
q = n \cdot e
q = (1 \times 10^6) \cdot (-1.6 \times 10^{-19})
= -1.6 \times 10^{-13}\,\text{C}
Unsolved Problems
Question 1: A body acquires a charge of +9.6 × 10⁻¹⁹. C. Calculate the number of electrons removed from it.
Question 2: Three particles have charges q1 = +2 C, q2 = −5 C, q3 = +3. C. Find the total charge of the system.
Question 3: A neutral metal sphere is touched by a rod carrying a charge of +6 × 10⁻⁶ C. After separation, the sphere acquires half of the rod’s charge. Find the charge acquired by the sphere.
Question 4: A neutral metal sphere is placed near a negatively charged rod. If 2×10 electrons move from the sphere to the ground, calculate the resulting charge on the sphere. (Given: e=1.6×10⁻¹⁹ C)
Question 5: Two isolated spheres, one with a charge of +8 C and the other with −3 C, are connected by a conducting wire. Find the final charge on each sphere after they are separated.