# Suggestions for practice problems in E&M

• IxRxPhysicist
In summary, the conversation was about a person working through electromagnetic books and asking for suggestions on physically insightful or useful problems. A list of suggested problems from Physics Forums was provided, along with a hint for an E&M problem involving the equations B=μ0H+M and ∇⋅H=ρmμ0. The solution to this problem involves an integral with an inverse square law, but the question was raised about where the current in conductor contribution to H is. Similarly, taking the curl of both sides of the equation also raises the question of the missing magnetic "pole" contribution.
IxRxPhysicist
Hey all,
I am working my way through a couple of emag books (Griffiths, Jackson, and Schwinger) and I was wondering if any of y'all have suggestions for problems that you thought were particularly physically insightful or useful.

Cheers,
IR

IxRxPhysicist said:
Hey all,
I am working my way through a couple of emag books (Griffiths, Jackson, and Schwinger) and I was wondering if any of y'all have suggestions for problems that you thought were particularly physically insightful or useful.

Cheers,
IR
Try these problems/posts that were recently on Physics Forums:
https://www.physicsforums.com/threa...field-of-a-uniformly-polarized-sphere.877891/

Logical Dog
@IxRxPhysicist I have one more E&M problem that I don't think is included in the above that you might find useful. Begin with the equation ## B=\mu_o H +M ## which is an equation that comes out of the "pole" model of magnetostatics. (J.D. Jackson emphasizes the "pole" model.) (Sometimes you will see this equation as ## B=\mu_o H +\mu_o M' ## where ## M'=M/\mu_o ##.) Upon taking the divergence of both sides ## \nabla \cdot B=\mu_o \nabla \cdot H +\nabla \cdot M ##. But ## \nabla \cdot B=0 ## so that ## \mu_o \nabla \cdot H=-\nabla \cdot M ##. You might recognize the right side as ## -\nabla \cdot M=\rho_m ## where ## \rho_m ## is the magnetic charge density (fictitious). The problem is to solve this for ## H ##. ##\\ ## The result is that ## H ## has an integral solution with the inverse square law ## H(x)=\int \frac{1}{4 \pi \mu_o} \frac{\rho_m(x')(x-x')}{|x-x'|^3} \, d^3x' ##. The question is, where is the current in conductor contribution to ## H ## which is absent from this solution? I will give you a hint: The inhomogeneous differential equation ## \nabla \cdot H =\frac{\rho_m}{\mu_o} ## can also have a solution to the homogeneous equation as the complete solution. (The current in conductor contribution to ## H ## can be found using Biot-Savart's law. The Biot-Savart solution obeys ## \nabla \cdot H=0 ##.) ## \\ ## Note: A similar problem is encountered if you take the curl of both sides of the above equation. ## \nabla \times B=\mu_o J_{total} ## (in the steady-state case) where ## J_{total}=J_{free}+J_m ## and ## \nabla \times M=\mu_o J_m ## so that ## \nabla \times H=J_{free} ##. This has a Biot-Savart type integral for ## H ##, but the question is where did the magnetic "pole" contribution go that we found above with the ## \nabla \cdot H ## equation? And the answer is again similar: This time, the homogeneous ## \nabla \times H =0 ## needs to be considered as having a contribution to the complete solution for ## H ##.

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## 1. What is the best way to practice solving E&M problems?

The best way to practice solving E&M problems is to start with basic concepts and gradually work your way up to more complex problems. It is important to understand the fundamentals before attempting more difficult problems. Also, make sure to practice regularly and seek help from a teacher or tutor if needed.

## 2. How can I find practice problems for E&M?

There are many resources available for finding practice problems in E&M. You can check your textbook, online study guides, or even search for practice problem books specifically for E&M. You can also ask your teacher or professor for additional practice materials.

## 3. How many practice problems should I do to prepare for an E&M exam?

The number of practice problems you should do to prepare for an E&M exam will vary depending on your level of understanding and the difficulty of the exam. It is recommended to do as many practice problems as possible, but make sure to focus on quality over quantity. It is better to fully understand a few problems than to rush through many without fully grasping the concepts.

## 4. How can I check my answers when practicing E&M problems?

You can check your answers by using the answer key provided in your textbook or practice problem book. You can also ask your teacher or professor for the correct solutions or seek help from a tutor. Additionally, there are online resources and forums where you can compare your answers with others and discuss different approaches to solving the problems.

## 5. Are there any specific tips for solving E&M problems?

Some tips for solving E&M problems include drawing diagrams to visualize the problem, breaking down the problem into smaller parts, and using unit analysis to check for mistakes. It is also helpful to practice using different problem-solving strategies and to understand the basic principles and equations used in E&M. Finally, make sure to read the problem carefully and double-check your work to avoid simple errors.

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