Fundamentals of Physics Chapter 21 Solutions: Coulomb’s Law
Halliday Resnick Fundamentals of Physics Volume 2 Solutions Chapter 21 is a perfectly curated guide for those aiming to clear prestigious competitive exams like JEE and NEET. In this chapter, you will learn about fundamentals of physics volume 2 laws and properties of an electric charge, conductor and insulators, Coulomb’s law and shell theories of electrostatics, elementary charge and its quantization, and conservation of charge.
This chapter has a total of 87 questions which are divided into 2 sets of ‘questions’ and ‘problems’. The problem set is further divided into modules that have questions based on specific concepts like finding the electrostatic forces, conservation of charges, the magnitude of the net electrostatic force on a particle due to another, the charge on an ion, and equilibrium. By solving these questions, you will be able to overcome many hurdles while preparing Physics for JEE and NEET.
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Important Topics for Halliday Resnick Fundamentals of Physics Volume 2 Solutions Chapter 21: Coulomb’s Law
The key ideas presented in Chapter 21 of Resnick Halliday Physics solutions of Physics Volume 2 will teach you the formula of coulomb’s law and how to find the net force between two particles. You will be able to identify how net charge in an isolated system is a constant and equilibrium of 2 forces on a particle.
- Electric Charge – Every matter has a property that can either repel or attract another matter around it; this is its electric charge and it determines its electrical interaction with other objects. An electric charge could be either positive or negative. Charges of the same type repel each other and charges which are opposite, attract each other. Electrically neutral objects are the ones that have equal amounts of positive and negative charges within them.
- Conductors – Objects which have a large number of freely moving electrons within them.
- Insulators – Objects which do not allow free movement of electrons by holding them in their orbit are insulators.
- Electric Current – The rate at which charge passes through a point is defined as an electric current and is given by:
i = dq/dt
Here i = electric current, q = electric charge, t = time.
- Coulomb’s Law – This law describes the electric force exerted by 2 charged particles (ch1 and ch2) on each other when they are separated by a distance d and are either at rest or moving slowly towards each other. It states that the magnitude of this electric force is:
o Inversely proportional to d2, where d is the distance between the point charges.
o Directly proportional to the magnitude of the charges multiplied together.
o The direction of force is on the line which joins the 2 points and could be either directed towards each other or away from each other.
F (force) = n ∣ ch1 ch2∣ / d2
Here n is the coulomb’s constant = 1/4π ε0 = 8.99 * 109 Nm2 /C2
ε0 = permittivity of space = 8.854 x 10-12 C2 N-1 m-2
Shell Theorems of Electrostatics –
- Theorem 1 – A shell that has a uniform charge would attract or repel any charged particle, outside its surface, as if the shell’s entire charge were concentrated at its centre.
- Theorem 2 – Any charged particle, which is inside the shell, does not experience an electrostatic force from the shell.
- The Charge is Quantized – The electric charge is restricted to certain values and is a multiple of the number of electrons in the object.
Charge = n * e
Here n is a positive or negative integer
e is the charge (a proton is + and electron -) = 1.602192 X 10-19
- The Charge is Conserved – For an isolated system, the net charge is always conserved and is a constant. The totals of positive and negative charges are the same in the universe always. This hypothesis was given by Benjamin Franklin. Radioactive decay of nuclei is an example of this where nuclei transform into different nuclei like Uranium-238 becomes Thorium-234 by the emission of an alpha particle which is Helium-4.
- Annihilation – When an electron and its antiparticle, positron, go through the process of annihilation, they become 2 gamma rays.
e– + e+ → ƴ + ƴ
- Pair Production – A gamma-ray transforms into an electron and a positron in pair production.
ƴ → e– + e+
Discussion of Exercises of Halliday Resnick Fundamentals of Physics Volume 2 Solutions Chapter 21: Coulomb’s Law
The first set of exercises has 12 questions based on the equilibrium of electric force and calculating force on a particle that is surrounded by other charged particles.
Module 1: Coulomb’s Law
Module 1 has 23 questions and is based on coulomb’s formula. Here you will find problems where along with coulomb’s law you would need to apply the law of equilibrium of 2 charged particles to solve different kinds of problems presented.
Module 2: Charge is Quantized
Module 2 has 12 questions which are based on the fact that charge is quantized. Here you get to solve problems where the number of electrons has to be determined in objects and the formula of the electrostatic force between objects.
Module 3: Charge is Conserved
Module 3 has only 2 questions based on conservation of charge where problems on radioactive decays are to be solved.
The last section has additional problems and has a total of 38 questions. It encompasses all the theories discussed in the chapter like the two shell theorems, Coulomb’s law, properties of an electric charge like quantization and conservation, nuclear transformations, electrostatic forces induced by charged particles, equilibrium separation, and formulas of electric charge.
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