Can someone please help me with this, I want it similar to the example I have posted down below. I need help with the summary and application part please

please take a look at the notes that I have posted, I want a summary and application related to the topic thats covered and I am a bit confused what application I could talk about or use.

Thanks

I have updated the notes for it below

Question:

A beam of protons travelling at 1.00 x 10⁵ m/s has a current density of 1.00 mA/m². What is the density of protons in the beam?

Answer:

6.25 x 10¹⁰ m^-3

Solution:

Density equation: ?=?/?=???_d

?=??/???

Solving for n now: n = 0.001?seccoulombs?/m2 / (1.602?10^-19protoncoulombs?)(1.00?10⁵ secm?)

n = 6.24????1010????3?

Example

Question: A 2.0 mm diameter wire made of unknown material carries a constant current of 1.0 A. What can you say about the current density in the wire? Summary: The main content required to solve this problem is an understanding of Ohm's Law, and what circumstances are required to use it. The equation here would be J = i/A, where J is the current density, i is the current, and A is the area. Solution: In this problem, we are able to replace A with pi/4dh2, given that i is 1.0 Amps and diameter is 2.0 mm. Hence. J = i/(pi/4dh2) = 1/(pi/4(4 mm)) = 3.18 E5 However, despite this information, we are not told enough about the material, so it could have a varying current density across the diameter of the wire. Our answer: There is not enough information to describe how, or if, the current density varies across the diameter of the wire. Application: We can apply the concepts of current density to conductors. In conductors. the current and current density are found to be proportional to the electric field. We can use this information to show that the current density is equal to the ratio of electric field strength to resistivity. as well as telling us how strong our electric field needs to be to produce a certain J. Sources: Electric Current, Current Density, Resistivity and Resistance. (2022, December 09). l120LecO9Current&Resistivity.pdf (wpi.edul Here is a summary of the main ideas in Chapter 26. 1. When charges move in a circuit, they form a current. Current is defined as the rate of change of the current - or dq . t . mathematically: 1, = E' orq : f0 1 dt. Since charge is conserved, then, current is also conserved in a circuit. Our convention for current is that it measures the motion of charge carrier. Thus. a positive current will flow from the positive end ofa battery, even though the charges that are moving (electrons) leave the negative end of a battery. We do this so that we can satisfy the idea that the electric potential drops around a circuit moving from the + side of the battery to the - side of the battery. . The current density is a vector with a magnitude equal to J : is where i is the current and Ais the cross-sectional > > area. It represents the flow of the current and can be written as: J : nevd where n is the number of charges per unit volume, e is the electric charge, andvd is the charge drift velocity. A positive electric field E will produce a movement of the positive charge carriers producing a positive current density J with the drift speed of the charges equal tovd. Ohm's law states that there is a linear relationship between the potential difference in a conductor and the current that flows. The proportionality constant is the resistance or R = Z. The resistance can also be written as R 2 pi, 'n'. where L is the length of the conductor. A is the cross-sectional area, and p is the resistivity. a property of the conductor. The inverse of the resistivity is the conductivity or p = i. In a conductor, since the product of the electric field and 0' > > length is the potential drop or E L = V. one can rewrite Ohm's law as: J 2 0E. We can understand how electrons move in a metal conductor if we think of them moving like they are nearly free particles like in a gas. If the electrons are accelerated by the applied electric field. before colliding with other atoms in the conductor we can write an expression for the acquired drift speed (average) motion of the electrons asmd = %'r, where T is the average time between collisions. Combining this relationship with the above equations allows us to write an expression for the resistivity of a material in terms of its microscopic properties. However, this drift speed is much less than the effective speed of the electrons (due to its thermal motion) which is many order of magnitude higher 1 million meters/sec The rate of transfer of energy in a conductor is equal to: P = iV. Since Ohms law is V = iR, Power can be rewritten: P 2 @212. Resources: Walter Lewin: Electron Current. resistivity, Ohm's Law Khan Academy: Ohm's Laws