Fundamentals of Physics Chapter 28 Solutions: Magnetic Fields
Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions for Chapter 28 ‘Magnetic Fields’ has all the concepts and formulas that will clear your basics for Class 12 exams and JEE and NEET. In Resnick and Walker Halliday Magnetic Fields you will learn topics like the difference between an electromagnet and a permanent magnet, how a magnetic field is a vector with magnitude and direction, find out the relationship between various factors when a charged particle moves through a magnetic field and describe J.J Thomson experiment. The HALL effect, the magnetic force on a current-carrying wire, torque on a current loop and the magnetic dipole moment on a current-carrying coil are some other important concepts of this chapter.
Resnick Halliday and Walker Fundamentals of Physics Volume 2 Magnetic Fields Solutions has a total of 104 questions divided into 9 sections. You will get ample practice on all the questions that can come in physics for JEE or NEET with these exercises. These questions need you to find the orientation of vector when a charged particle moves through a magnetic field, find the magnitude of electric potential in a current-carrying wire in a magnetic field, find which force dominates when a charged particle is moving in 2 opposing electric and magnetic fields, calculate speed and kinetic energy of an alpha particle travelling in a circular path in a uniform magnetic field.
Resnick Halliday and Walker Fundamentals of Physics for JEE is a must-have book for students who are aspiring for tough engineering entrance exams since it has unique content meant for these exams. Our team has strived to give you Solutions for the Halliday Resnick and Walker Magnetic Fields chapter in an easily comprehensible manner which helps you get a clear understanding of the concepts so that you can manage your time better with even complicated problems.
Important Topics for Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions Chapter 28: Magnetic Fields
- Magnetic Field – If a charged particle with charge ch is moving with a velocity of v in a magnetic field which has a force F then the magnetic field M is given by :
= ch( X )
The unit of the magnetic field is tesla (T).
1 T = 1 N/(A. m) = 104 Gauss
Here N = Newton, A= coulomb per second, m = meter
- Crossed Fields and Canceled Field – If a particle moves in both electric and magnetic fields, then it gets affected by both the fields.
- If these fields are perpendicular to each other then they are called crossed fields.
- If these fields are in opposite directions so that the net effect on the particle is zero and there is no deflection then they are cancelled fields.
We can measure the speed of the particle when placed in 2 fields by:
v = E / M
Here v = velocity of the particle
E = Electric field
M = Magnetic field
- The Hall Effect – If a conducting strip with current i is placed in a uniform magnetic field of magnitude and both current and the field are perpendicular to each other, then there is built up of some charge carriers (ch) on one side of the strip, and a potential difference V occurs across the strip. The electric force gets balanced by magnetic force and the number density (n) of the charge carriers is given by:
n = i/ (V l ch), Here l is the thickness of the strip parallel to
- Charged particle in a magnetic field – A charged particle, with mass m and charge magnitude |ch|, moving with velocityin a uniform magnetic fieldcan travel in a line, circular path or a helical path based on certain conditions. If it is moving perpendicular to the field then going by Newton’s 2nd law of circular motion :
|ch| **= (m *2) / r
Here r is the radius of the circular path = (m *) / |ch| *
If f is the frequency of revolution, w the angular frequency and T is the period of motion then: f = w/2π = 1/T = (|ch|) / 2πm.
- Cyclotrons and Synchrotrons – High energy particles like electrons and protons have been used to probe atoms and nuclei and figure out the fundamental structure of matter.
- Cyclotrons – Charged particles that are accelerated by electric force and circling in the magnetic field make a cyclotron. Its operation depends on the fact that the frequency (that is independent of its speed) of its circulation in a magnetic field is equal to the frequency of the electrical oscillator, which is fixed.
F = fosc ( this is also called the resonance condition)
- Synchrotrons – Cyclotrons fail at very high speed since the fundamental of their formation is true only for particles which have speed less than that of light. Synchrotrons solve this by varying the magnetic field and fixed frequency fosc, with time, in the accelerating cycle and the path of the particles is circular, not spiral.
- Magnetic force on a current-carrying wire – A sideways force is experienced by a straight wire which is carrying current i in a magnetic fieldis given by:
= i X,
And the force experienced by a current element, id, in the magnetic field is:
Hereor dis the length vector of the current-carrying wire which is in the direction of the current
- Torque on a current loop – If a coil, carrying current i with N number of turns and each turn has an area A, is placed in a uniform magnetic field, it will experience a torque that is given by:
Here, is the magnetic dipole of the coil = NiA and its direction is given by the right-hand rule.
- Orientation energy of a magnetic dipole – A dipole in an external magnetic field experiences energy which depends on the dipole’s orientation in the field. It is given by:
Here – dipole moment
– Magnetic field
θ – angle the dipole makes with the magnetic field
- Work is done by an external agent in moving a dipole – If an external agent rotates a magnetic dipole from orientation θa to θb so that the dipole is stationary initially and finally, then the work done by the external agent in doing this is given by:
Wa = Ub – Ua
Discussion of Exercises of Resnick Halliday and Walker Volume 2 Solutions Chapter 28: Magnetic Fields
The first section has a total of 12 problems. You would need to find out the magnitude and direction of charged particles in a magnetic field, solve sums on the concept of crossed fields, Hall Effect, and orientation energy of magnetic dipole moment.
Module 1: Magnetic Fields and the Definition of B
Module 1 has 6 questions in which you would have to calculate the speed and energy of charged particles in a magnetic field. The charged particle could be an electron, proton, or an alpha particle.
Module 2: Crossed Fields: Discovery of the Electron
Module 2 has 6 questions on the concept of crossed fields. You will be given certain values like velocity and acceleration for an electron or proton travelling in a magnetic field and would require finding out the electric or magnetic field on it, or vice versa.
Module 3: Crossed Fields: The Hall Effect
Module 3 has 4 questions based on the Hall Effect. In these questions either a metal strip, a conductor, or a metallic block are moving in a magnetic field and you either have to calculate the potential difference, electric field, or the velocity.
Module 4: A Circulating Charged Particle
Module 4 is dedicated to problems on circulating charged particles and has 18 questions. Here you would need to calculate various parameters like the speed, kinetic energy, period of revolution, etc. for charged particles moving in a circle within a magnetic field.
Module 5: Cyclotrons and Synchrotrons
Module 5 has 4 questions on cyclotrons and synchrotrons. You will be given values for a magnetic field or potential difference and need to calculate resonance condition values, oscillator frequency or the total path length travelled.
Module 6: Magnetic Force on a Current-Carrying Wire
Module 6’s key concept is the magnetic force on a current-carrying wire and has 10 questions. This section tests your knowledge on how to calculate the magnitude and direction of the magnetic force on a wire in many different scenarios.
Module 7: Torque on a Current Loop
Module 7 has 5 questions. You need to apply formulas related to the torque on a current loop in a magnetic field to solve these problems.
Module 8: The Magnetic Dipole Moment
Module 8 is based on the magnetic dipole moment and has a total of 12 questions. You would get practice on calculating orientation energy of a dipole and work done by external force on moving a dipole, in these sums.
The last section has 23 additional problems comprising almost all the concepts discussed in this chapter. There are sums on torque on a current loop, the magnetic force on a current-carrying wire, charged particle in a magnetic field, Hall effect, cyclotrons and synchrotron.
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