Fundamentals of Physics Chapter 24 Solutions: Electric Potential
Halliday Resnick & Walker Fundamentals of Physics Volume 2 Solutions for Chapter 24 ‘Electric Potential’ is the ultimate source if you are willing to do well in your Physics Exam. By doing Practice with our Resnick Halliday Walker solutions Volume 2 Solutions for Electric Potential, you will be able to solve all the questions of the chapter by yourself. This chapter includes topics like electric potential and electric potential energy, equipotential surfaces, the potential from the field, potential due to a charged particle and potential due to an electric dipole.
Resnick Halliday and Walker Volume 2 Solutions for Electric Potential has 67 questions in total with some additional problems as well. They are settled in 8 different Modules. Practising it you will definitely get benefited and all your concepts regarding this chapter will be brightened. You will be able to see how electric force is conserved and possesses potential energy and understand the relationship between a charged particle at a point and the potential energy of a system.
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Important Topics For Halliday Resnick & Walker Fundamentals of Physics Volume 2 Solutions Chapter 24: Electric Potential
In this chapter of Halliday Resnick and Walker Fundamentals of Physics Volume 2 book, you are going to study some beautiful and important concepts of electric potential. Starting from different energies like electrical potential energy and mechanical energy, you will understand what are Equipotential surfaces?. Further, you will derive the electric potential due to a charge, also due to an electric dipole. Apart from this, you will introduce the electric potential due to a continuous charge distribution, and electric potential energy of a system of charged particles as well.
Let’s see a definition of a few of them so that you could understand what this chapter is going to teach you.
What is Electric Potential?
An electric potential is nothing, it’s the amount of work that is needed for moving any charge inside the electric field from a particular point to the specific point. Typically, here the point is the earth or can say infinity. However, It is not mandatory, any reference point can be used.
Here’s the general formula –
V = Energy / charge
V = W / q
Its S-I unit is volt and in terms of dimensions, is M L^{2} T^{-3} I^{-1}
- Electrical Potential Energy-
Like, you know the electric potential is the amount of work needed for moving a charge from one reference point to a specific point. However, if we talk about electrical potential energy, the only difference is that amount of work is needed to move a charge against the electric field.
If q is the charged particle at any point where the electric potential is V. Thus, the electric potential energy U between the potential difference ΔV is-
W = – q ΔV
Its S-I unit is the Joule.
- Mechanical Energy-
In simple words, Mechanical Energy is the summation of Kinetic Energy and potential Energy.
If we talk about the Charge particle is moving with the change in electric potential ΔV without any force, then applying the law of conservation of mechanical energy gives the change in kinetic energy is –
Δ K = -q ΔV
On doing work W, the change in kinetic energy becomes –
Δ K = -q ΔV + W
In some special cases when Δ K = 0, then the work is done is equal to-
W = q ΔV
- Electric Potential due to a point charge-
Well, the electric potential (VE) due to a point charge (Q) at some distance ‘r’ is –
- Electric Potential due to an Electric Dipole-
Electric Potential at some distance r from an electric dipole with the dipole moment magnitude P= 2r is given here-
From above we can deduce that-
Electric potential is inversely proportional to the square of the distance from an electric dipole- V∝ 1/ r^{2}
- Electric Potential due to the continuous charge distribution-
Electric potential due to the continuous charge distribution is –
V = 1/ 4π ε0 ∫ dq / r
- Electric Potential Energy of a system of a charged particle-
The Electrical potential energy of a system of a charged particle is given here-
U = W = 1/ 4π ε0 [ q1 . q2 / r ]
Where U is the electric potential energy of a system of a charged particle.
Exercise Discussion of Halliday Resnick & Walker Class 12 Volume 2- Solutions Chapter 24- Electric Potential
Module 1: Electric Potential
Module-24.1 has only 3 questions based on the electric potential and potential difference between two points. These questions are simple to solve; you need to implement the formula of an electric potential.
Module 2: Equipotential Surfaces and the Electric Field
In Module-24.2, there are 8 questions. For solving them, you need to have knowledge about Equipotential surfaces and electric fields. In most of these questions, you have to determine the electric potential differences, and electric field at some point.
Module 3: Potential Due to a Charged Particle
Module-24.3 of Resnick Halliday and Walker Class 12 Volume 2- Solutions Chapter 24 has 9 odd questions. They are using the concept of potential due to a point charge.
Module 4: Potential Due to an Electric Dipole
Well, Module-24.4 contains only 2 questions based on the concept of the electric potential due to an electric dipole. In these questions, you have to compute the electric potential of any molecule due to an electric dipole at some distance r.
Module 5: Potential Due to a Continuous Charge Distribution
There are 11 Resnick Halliday and Walker problems for Electric Potential in module-24.5 of this chapter. You need to brush up your knowledge on the potential due to the continuous charge distribution to tackle the questions of it.
Module 6: Calculating the Field from the Potential
The next set of 7 questions in the module-24.6 is about finding the electric field from potential. You will have to find an electric field in the plane. In some cases, you are given the electric field in a plane and you have to calculate the coordinates of the plane.
Module 7: Electric Potential Energy of a System of Charged Particles
In module-24.7, there are 21 total questions. You have to find the electric potential energy of a system of charged particles.
Module 8: Potential of a Charged Isolated Conductor
And, in the last module-24.8 has 7 such questions based on the concept of the potential of a charged isolated-conductor. There are questions where you have to find the potential of a sphere, ratio of surface densities of a sphere and electric potential at the centre of the sphere.
Besides these questions, there are some more 36 problems that aid you to grasp the concepts of the chapter easily.
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