# Fundamentals of Physics Chapter 29 Solutions: Magnetic Fields Due to Currents

Resnick Halliday & Walker Volume 2 Solutions Chapter 29 ‘Magnetic Fields due to a Current’ are designed by subject matter experts for easy JEE and NEET preparations. These solutions will give you in-depth knowledge of magnetic fields set up by a current-carrying conductor. You would learn about the Biot-Savart law and how a moving charged particle creates a magnetic field around it, what happens when 2 current-carrying wires are together in a magnetic field, how is the force exerted on 2 parallel current-carrying wires when current is in opposite direction and also in the same direction, Ampere’s law, describing solenoids and toroids, and what is the magnitude and direction of the field exerted by a current-carrying coil (which is a magnetic dipole) in a magnetic field.

Resnick Halliday and Walker Physics Volume 2 Magnetic Fields due to Current Solutions include 99 questions divided into 7 modules. These problems are on the lines of the kind of sums that come in Physics for JEE or NEET. The many exercises will have questions where you would calculate the magnetic field due to a current in a straight wire and in a circular arc of wire, apply ampere’s law to a loop that encircles a current, calculate field inside a solenoid, calculate the dipole moment of a current-carrying coil.

The level of questions in Resnick Halliday & Walker Fundamentals of Physics is completely oriented towards competitive exams. Solutions for Halliday Resnick and Walker Magnetic Fields due to a Current given by our team will not only help in solving the problems but also clear the concepts in a way that will make you adept in solving various kinds of problems that can come in the JEE Mains, JEE Advanced and NEET kind of entrance exams.

## Important Topics for Resnick Halliday & Walker Fundamentals of Physics Volume 2 Solutions Chapter 29: Magnetic Fields due to a Current

**Biot-Savart** **Law**– This law gives the formula to calculate the magnetic field that a current-carrying conductor sets up. If a current element *id *is at a distance d from a point P then the field dM produced by this current element is given by:

Here 0 = permeability constant = 4 π x 10^{-7} T * m/A

**-the unit vector which points from the current element towards the point**

**Right-hand Rule –**To find out the direction of the magnetic force on a positive moving charge, point the thumb of your right hand in the direction of the velocity of the particle, fingers in the direction of the magnetic field then the direction of the force is perpendicular to the palm.**The Magnetic Field of a Long Straight Wire –**A long straight wire carrying a current i exerts a magnetic field at a point P which is at a perpendicular distance d from it, given by:

**The Magnetic Field of a Circular Arc –**For a point in a curved wire carrying current, you can find the magnetic force at a point by finding the magnitude of a single current length element and then integrating it for all current length elements to find the net field. If the circle has radius r and central angle θ, then magnetic field at its centre by a current i is given by:

**Force Due to Current in Parallel Wires –**Wires parallel to each other and carrying current i will attract each other if the current direction is the same and repel if currents are in opposite directions. We can find out the magnitude of the force on length L in either wire separated by distance d and having current i_{x}and i_{y}as given by below formula:

**Ampere’s Law – The net electric field due to a distribution of charges can be obtained by finding the differential electric fielddue to one charge element and then summing up across all charge elements. Ampere law gives this formula for a closed-loop as below:**

Here the circle around integration sign denotes that summation is done around a closed loop which is called the Amperian loop and i_{enc} is the total current enclosed by the loop.

**Solenoid and Toroid fields – **

- A long tightly wound helical coil of wire is called a solenoid. The magnetic field in a solenoid having n number of turns per unit length and carrying current i, not near its end is given by:

- A toroid is a hollow solenoid which is curved to make its 2 ends meet. The magnetic field at a point inside a toroid is given by

Here d is the distance of the point from the centre

**Field due to a Magnetic Dipole –**If a coil with N number of turns and each turn has an area A is carrying current I and is placed in an external magnetic field, then it behaves as a magnetic dipole whose torque is given by:

Here isthe magnetic dipole of the coil = NiA and its direction is given by the right-hand rule.

The magnetic field produced by this coil at a point P which is at a distance d along the coil’s perpendicular central axis is given by:

Here – dipole moment

– Magnetic field

0 – permeability constant

### Discussion of Exercises of Halliday Resnick and Walker Volume 2 Solutions Chapter 29

**Questions **

The first section has a total of 11 problems. In these you need to apply your knowledge of calculating the magnetic field to rank some situations based on their magnetic field intensity, these fields could be along wires or circles or Amperian loops.

**Module 1: Magnetic Field Due to a Current**

Module 1 is based on the concept of the magnetic field due to a current and has a total of 34 questions. There are questions on the application of Biot-Savart law to earth’s magnetic field, magnetic compass, hairpin conductor, and miscellaneous kinds of objects. There are questions where you need to find a point in the field where there is the greatest force or some percentage of the force.

**Module 2: Force Between Two Parallel Currents**

Module 2 has 7 questions around parallel currents and force between them. You need to find things like the x component of magnetic current per unit length, in some, there are 3 wires where the direction of current is to be found.

**Module 3: Ampere’s Law**

Module 3 has 7 questions on Ampere’s law. The questions test your expertise in varied ways. You need to calculate the magnetic field at radial distances given, the value of the integral along a closed path around conducting loops, etc.

**Module 4: Solenoids and Toroids**

Module 4 is based on solenoids and toroids and has 7 questions. You need to find the magnetic field inside a toroid or solenoid, inner and outer radius, and the number of turns an electron in a solenoid makes before exiting.

**Module 5: A Current-Carrying Coil as a Magnetic Dipole**

Module 5 has a total of 8 questions where you need to apply formulas of a current-carrying magnetic dipole. There is a question on Helmholtz coil where you have to find the magnitude and direction of magnetic dipole and there are square current loops for which you have to calculate the magnitude of the net magnetic field at various coordinates.

The last section is additional problems which are an amalgam of most of the topics discussed in this chapter and has 23 questions. It involves calculations for magnetic field intensity and direction for a long straight wire, application of Ampere’s and Biot-Savart law, and current-carrying parallel wires sums.

## Why Use Resnick Halliday & Walker Fundamentals of Physics Volume 2 Solutions Chapter 29: Magnetic Fields Due to Electric Current by Instasolv?

- We have an academic team of experts who know what it takes to prepare for exams like NEET and JEE hence we have prepared Resnick Halliday and Walker fundamentals of physics volume 2 solutions in-line with the standards.
- By seeking the help of our solutions you would learn many tips and tricks to memorize the formulas so that you do not have to bother about managing time in the stressful exam situation.