Can someone please help me with the summary part and application part, please

I have attached an example of what it should be as well as the notes.

Question:

The figure below shows a circular region of radius R=0.100?m with a time-varying magnetic field of magnitude B=b?t which points into the page. If b=6.03?T/s, what is the magnitude of the electric field at r=0.442?m?

Solution:

E2?r=dtd?B??=dtd?(B?A)=dtd?(bt?R2)=b?R2

E=2rbR2?=2(0.442m)6.03T/s(0.100m)2?=0.0682V/m

E x 2??r = d??B / dt = d? / dt?(B??A?)=d? / dt??(b?t??R2)=b??R2.

Solving for E and plugging in the given values

ar

E?=b?R²/ 2r

=(6.03?T/s)(0.100?m)² / 2(0.442?m)

=0.0682?V/m

Summary

Example:

Question: A circular surface lies perpendicular to an electric field which is uniform across the surface but increases in strength at a constant rate over time. During this same time interval, the induced magnetic field within the surface Summary: This problem deals with the relationship between electric fields and the induced magnetic fields on within the same region. We will explore this relationship by looking at Maxwell's Law of Induction, doE d(EA) f B . ds = MOE0 dt = HOEO dt Solution: Using the equation above, we can see that if the Electric field increases at a constant rate, then the derivative of the Electric field is constant. This means that the induced magnetic field will be constant. Application: An application of induction, is induction cap sealing. This works by generating an electromagnetic field that interacts and heats up the foil of the seal. This heat causes the foil to begin to melt slightly, which seals the container as it is cooled down. Reference: How Induction Sealing Works? Pillar Technologies. https://www.pillartech.com/induction-sealers/resources/how-induction- sealing-works (Accessed 12 July 2023)Here is a summary of the material in Chapter 32 1. You will recall that Gauss's law of electric charges states that the electric flux through a closed surface is proportional to the charge contained within that surface. For magnetism, because there is always a north and south pole for a magnetic, the magnetic flux through a closed surface is always zero. Thus, there is never a magnetic monopole. This can be Written as of B - dA = 0 2. There is a parallel in magnetism to Faraday's Law. You will recall that if you have a changing magnetic flux you will induce an electric field around a closed loop. Maxwell's law states that a change in electric flux will produce a magnetic field around a closed loop. This can be written as f B . ds = HOEo dt de E That means as the electric field changes in time, a magnetic field will be produced. One can combine Maxwell's Law with Ampere's Law (from a previous chapter) to write what is known as the Maxwell -Ampere Law of B . ds = Moco at deE + Moiinc. If the electric flux is constant, then the field produced is just due to the current that is enclosed by integral on the left. However, the change in the electric flux will produce a term that looks like a current. This is often called the displacement current and is given by id = 80 at deE 3. Maxwell's equations are the 4 equations that describe all of the electric and magnetic field behavior. These were given in this week's kickoff announcement. 4. The earth has an intrinsic magnetic dipole field. The magnetic north pole is actually a south pole by convention. 5. An electron has a quantum property of spin angular moment (associated with its spin angular moment) which gives it a magnetic dipole moment. This spin is quantized, which means it can only take on certain values. Just as a magnetic dipole will react when placed in a magnetic field, an electron will do the same. 6. When an electron is in an atom, it also has an additional angular moment called the orbital angular momentum which gives it an additional magnetic dipole moment. The values of this orbital angular momentum are also quantized. Thus an atom will react when placed in a magnetic field. 7. There are three types of magnetic materials: diamagnetic materials have very small dipole moments and produce a weak reaction when placed in a magnetic field, paramagnetic materials have a randomly directed permanent dipole moment that can align when placed in a magnet field and Ferromagnetic materials have an aligned permanent dipole moment. They're magnetic dipole moment can be enhanced by placing them in an external magnetic field. Resources Walter Lewin Maxwell Equation and Magnetic materials Walter Lewin Ampere's Law Walter Lewin Displacement Current Crash Course Physics Maxwell's Equations