Coulomb's Law
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| Coulomb's Law |
"The force of interaction between any two charges is directly proportional to the multiplication of the charges and inversely proportional to the square of the distance between them."
(or)
The force of attraction or repulsion acting along a straight line between two electric charges is directly proportional to the product of the charges and inversely to the square of the distance between them.
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| Coulomb's Law |
`F \prop \frac{1}{r^2}` ..........eq. (2)
Combine eq. (1) and eq. (2)
`F \prop \frac{q_1q_2}{r^2}`
`F = \frac{K q_1q_2}{r^2}` ..........eq. (3)
Where
K = Electrostatic Constant (or Coulomb Constant)
`K = \frac{1}{4\pi \epsilon_0}`
`K = 9 \times 10^9 \frac{N m^2}{C^2}`
`\epsilon_0 = \text{Electrical permittivity of free space}`
`\epsilon = 8.854 \times 10^{- 12} \frac{C^2}{N m^2}`
Units and Dimension of K
From eq. 3
`F = \frac{K q_1q_2}{r^2}`
`K = \frac{F r_2}{q_1 q_2}`
Thus, units of the Coulomb Constant K
`K = \frac{N m_2}{C_2}`
For dimension of Coulomb Constant K
`K = \frac{F r_2}{q_1 q_2}`
`K = \frac{[M^1 L^1 T^{-2}] [L^2]}{[A^1 T^1] [A^1 T^1]}`
`K = [M^1 L^3 T^{-4} A^{-2}]`
Units and Dimension of `\epsilon_0`
`\epsilon_0 = 8.854 \times 10^{- 12} \frac{C^2}{N m^2}`
`\epsilon_0 = \frac{1}{4 \pi K}`
`\epsilon_0 = \frac{1}{[M^1L^3T^{-4}A^{-2}]}`
`\epsilon_0 = [M^{-1}L^{-3}T^{4}A^{2}]`
Limitation of Coulomb's law
(i) It is used only for static charges (Charges at rest).
(ii) Coulomb's law is true only for point charge (very small charges).
(iii) Separation between charges should not be very large.
(iv) Separation between charges should not be very small.
Electroscope
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| Electroscope |
There is a glass jar in a gold leaf electroscope in which a metallic rod is placed vertically. There is a metallic disc on the upper end of the rod whereas there are two gold strips tied at the lower end. When a charged body is taken to be in contact with the metallic disc, then some of the charge gets transferred to the gold strips and the metallic (gold) strips move away from each other. If a charged body is taken towards the already charged electroscope and if the charges on the body and the electroscope are of same kind, then the gold strips repel each other and move away from each other. If the body and electroscope have unlike charges, then the gold strips attract each other.
Unit of Charge
The S.I. unit of charge is coulomb (C). It is represented by C.
The formula of electric charge
`\text{Charge} = \text{Current × time}`
`Q = I \times t`
Thus, the dimensions of electric charge,
`Q = [M^0L^0T^1A^1]`
Since Coulomb is a large unit. Thus, the units of charge can be represented as follows
`1 \mu C = 10^{-6} C`
`1 n C = 10^{- 9} C`
`1 p C = 10^{-12} C`
The unit of charge in the CGS system is stat Coulomb of Franklin.
`1 C = 3 \times 10^9` esu
The other unit of charge is Faraday (not Farad) where
1 F = 96500 C
Q. What is the SI unit of electric charge?
Ans. The SI unit of electric charge is the Coulomb and it is represented by the symbol C.
Q. What is the formula to find the electric charge?
Ans. The formula of electric charge is Q = I`\times`t
Q. Define electric charge.
Ans. Electric charge is the property of subatomic particles that lets them experience a force when placed in an electric and magnetic field.
Properties of Charge
There are two types of charges one is positive and the other is negative charge. Like charges repel each other and unlike charges attract each other.
Here are some important properties of electric charge -
Additivity of Electric Charge
The total charge on a system is equal to the algebraic sum of all the charges present in it.
For example
Adding four charges on a body +4q, - 5q, +6q, and +3q, we get +8q. If the sum total of the charges on the body is zero, then that body is said to be neutral.
Invariance of Electric Charge
The value of the electric charge (q) of a particle does not depend on the speed of the charge.
Charge at rest = Charge in motion
The ratio of charge of a particle (q) and its mass (m) is called a specific charge `(\frac{q}{m})`.
Conservation of Electric Charge
According to the conservation of electric charge, “Charge can neither be created nor be destroyed, but can only be transferred.”
Examples :
We can take an example of friction electricity. Before friction, the glass rod and silk cloth are neutral. On rubbing them together, the glass rod develops a positive charge and the silk cloth develops the same amount of negative charge on it. In this process the electrons from the glass rod transfer to the silk cloth. Thus, the silk cloth becomes negatively charged and the glass becomes positively charged. Here glass rod and silk cloth are a system that becomes charged and the total charge of the system is zero.
Quantization of Charge
According to quantization of charge, “ The electric charge is an integral multiple of an elementary charge `(e = 1.6 \times 10^{-19} C)`.” Thus, the possible charge on a body can be
`q = \pm` `n e`
(i) The charge `\pm` 1.3 e, `\pm` 1.6 e,`\pm` 2.4 e,`\pm` 4.8 e,`\pm` `\frac{1}{3}` e,`\pm` `\frac{2}{5}` e are not possible.
(ii) The minimum value of charge is `1.6 \times 10^{- 19} C`.
(iii) The quantum of charge is e.
Some Important Facts Related to Charges
(i) Charge is always related to mass. This means that the existence of a charge is not possible without mass but mass is possible without charge. A photon is a massless and chargeless particle. Neutron has mass but zero charges. But, every charged particle has some mass.
(ii) Charges at rest form an electric field, and charges in motion form an electric as well as a magnetic field. If the speed of charges is accelerated, then electromagnetic radiation is around the surroundings.
Coulomb's Law Questions
Q. Tow point charges A and B having charges `+ Q` and `- Q` respectively, are placed at a certain distance apart, and the force acting between them is F. If 25 % charge of A is transferred to B, then the force between the charges becomes.
(a) `\frac{9 F}{16}`
(b) `\frac{16 F}{9}`
(c) `\frac{4 F}{3}`
(d) F
Q. A total charge Q is broken into two parts `Q_1` and `Q_2` and they are placed at a distance R from each other. The maximum force of repulsion between them will occur, when
(a) `Q_2 = \frac{Q}{R}, Q_1 = Q - \frac{Q}{R}`
(b) `Q_2 = \frac{Q}{4}, Q_1 = Q - \frac{2Q}{3}`
(c) `Q_2 = \frac{Q}{4}, Q_1 = Q - \frac{3Q}{4}`
(d) `Q_1 = \frac{Q}{2}, Q_2 = \frac{Q}{2}`
Ans.
(d) `Q_1 = \frac{Q}{2}, Q_2 = \frac{Q}{2}`
Q. Two charges +2 C and +6 C are repelling each other with a force of 12 N. If each charge is given - 2 C charge, then the value of the force will be :
(a) 4 N (attractive)
(b) 4 N (Repulsive)
(c) 8 N (Repulsive)
(d) Zero
Ans.
(d) Zero
Questions and Answers
What is Coulomb's Law?
What is the formula for Coulomb's Law?
What does `q_1` and `q_2` represent in Coulomb's Law?
What does r represent in Coulomb's Law?
What is k in Coulob's Law?
What are the properties of electric charge?
Give an example of the conservation of electric charge.
What are the limitations of Coulomb's Law?
What is the unit of electric charge in the CGS system?
Questions for You
Q. Is repulsion a true test of electrification?
Q. Why repulsion is the only test for electrification?
Numerical Questions on Coulomb's Law
Chapter 1: ELECTRIC CHARGE AND FIELDS
PHYSICS NOTES
- Electric Charge, Basic Properties of Electric Charge, Conductors and Insulators, and Methods of Charging
- Continuous Charge Distribution
- Coulomb's Law, Electroscope, Properties of Charge, Quantization of Charge.
- Coulomb's Law in Vector Form
- Principle of Superposition of Charges
- Electric Field and Field Lines, Types of Electric Field, Electric Field Due to a Point Charge, Electric Filed Due to a System of Charges, Electric Field lines and their Properties
- Gauss's Law of Electrostatic, Definition of Gauss's Law, Formula, Electric Charge and its Four Properties, Applications of Garss's Law, Gauss's Law, and Important Points
- Prove of Gauss Theorem in Electrostatics
- Electric Field due to Conducting Sphere
- Electric Field due to Conducting Hollow Sphere
- Electric Field due to Non-Conducting Sphere
- Electric Field due to Infinitely Long Charged Wire
- Electric Field due to Infinite Conducting Sheet of Charge..
- Electric Field due to Non-Conducting Plane Sheet
- Electric Flux
- Definitions of Electric Dipole, Electric Field due to Electric Dipole on Axial Line..
- Electric Field Due to Electric Dipole on Equatorial Line
- Torque on a Dipole in Uniform Electric Field
- Work Done in Rotating a Dipole..
- Dielectric Constant
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