Work done by Electromagnetic Field II Energy of a continuous charge Distribution

Summary

In this video, the speaker introduces the concept of work done by an electromagnetic field, explaining the basic formulas and theory behind it. They discuss the oscillating nature of electric and magnetic fields, how energy is carried by these fields, and the key equations related to work done. The speaker also covers how to derive these formulas for exams, depending on the marks allotted, and provides detailed explanations on handling different cases. Viewers are encouraged to watch previous videos for a comprehensive understanding and to subscribe for more educational content.

Takeaways

• 📚 The video introduces the topic of work done by electromagnetic fields.
• ⚡ The instructor has already covered Maxwell's equations and the introduction to electromagnetic theory in previous videos.
• 🧲 Electromagnetic waves are oscillating electric and magnetic fields, and they carry energy.
• 🔧 Work done is the product of force and displacement, and this principle is applied to electromagnetic fields.
• ✍️ The formula for work done by electromagnetic fields is: W = (1/2) ε₀E² + (1/2) B².
• 📖 For exam purposes, students should know how to derive this expression, especially for questions worth more points.
• 🔍 The concept involves calculating the work done separately for electric and magnetic fields and then adding them.
• 🔢 For continuous charge distributions, summations are replaced by integrals to calculate work done.
• ✒️ Using Gauss's divergence theorem, volume integrals can be converted into surface integrals in certain cases.
• ✅ The final result for work done by an electromagnetic field can be written as W = (1/2) ε₀ E² + (1/2) B².

Q & A

What is the main topic of the video?

The main topic of the video is the work done by the electromagnetic field.

What should viewers do if they haven't watched the previous videos?

Viewers should watch the previous videos on Maxwell's equations and the introduction to electromagnetic theory, which are linked in the description box.

What is the basic formula for work done by a force in displacement?

The basic formula for work done is Force multiplied by Displacement.

What is the final expression for the work done by the electromagnetic field?

The final expression for the work done by the electromagnetic field is given as (1/2) * (ε₀ * E² + (1/μ₀) * B²).

How can work done by the electromagnetic field be found according to the script?

Work done by the electromagnetic field can be found by calculating the work done by the electric field and the magnetic field separately, then adding them together.

What should you do if a short question about the work done by the electromagnetic field is asked in an exam?

If a short question is asked, you should write the basic expression for the work done by the electromagnetic field.

What is necessary if a detailed derivation of the work done by the electromagnetic field is required?

If a detailed derivation is required, you need to show the work done by the electric field first and then by the magnetic field, and then combine the results.

What is the significance of using a potential 'V' when dealing with charges in a conductor?

Using a potential 'V' causes the charges to assemble in an organized manner, which is necessary for calculating the work done to move these charges.

How can the summation of charges be replaced if the charge distribution is continuous?

If the charge distribution is continuous, the summation can be replaced by an integral.

What is the importance of the divergence theorem in deriving the work done by the electromagnetic field?

The divergence theorem is used to transform the volume integral into a surface integral, which simplifies the calculation of the work done by the electromagnetic field.

What happens to the first term in the final expression when increasing the volume?

The first term becomes negligible in comparison to the second term as the volume increases.