Chapter 8: Electricity and magnetism (C6618773)

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Electricity is the presence and flow/movement of electric charges. Electric charge, though not definable, can either be positive or negative charge. The SI unit of electric charge is the coulomb (C). Charge conservation is the principle that the net charge of the universe is 0, and this cannot be changed, since unequal electric charge can neither be created nor destroyed.

Charges exert forces on each other, in accordance with the axiom â€œlike charges repel, and opposite charges attractâ€, at the quantity expressed by Coulombâ€™s law, $F=\dfrac{kq_{1}q_{2}}{r^2}$, where $k$ is Coulombâ€™s constant $k=8.988\times 10^9 Nm^2 C^-2$, $q$ are the respective quantities of charge, and $r$ is the distance between the centers of charge (analogous concept to center of gravity). The axiom is demonstrated, by that, like charges in-multiplied produce a positive [and therefore repelling] force; and unlike charges in-multiplied produce a negative [and therefore attractive] force. Note that the formula for Coulombâ€™s law is analogous to Newtonâ€™s law of universal gravitation, as it is a type of inverse square law, expressed as where intensity is inversely proportional to distance squared.

â€œThe whole like charges repel, unlike charges attract reminds me of homosexuality,â€ Kim remarked, â€œWhy do Christians see homosexuality as wrong?â€

â€œAs with any Sin,â€ Mandy remarked, â€œthere are multiple reasons. But prima facie, we can simply say the Bible says so in Romans 1:24-29 and 1 Corinthians 6:9-10. Although enlisted alongside greed and covetousness, the question is not necessarily whether you engage in that conduct, but whether you care if itâ€™s wrong, care what God says, and make no reasonable attempt not to do that thing [and discourage others].â€

â€œTo explore it deeper,â€ Kim asked, â€œWhy is it wrong?â€

â€œTwo reasons: (1) In the beginning, God made man and woman to become one flesh, so thatâ€™s Godâ€™s way of doing sexuality, so trying to do sexuality another way is a distortion,â€ Mandy replied, â€œAlso, (2) in Romans 1, Paul explores homosexuality as the exchanging of the glory of God, for, perhaps what is your most cherished idol, which is yourself. So in fact, homosexuality is self-idolization. This is congruous with Romans 1:24-29, which re-emphasizes the word â€œexchangeâ€.

â€œMarriage should be between a man and a woman,â€ Em said.

â€œThat comment was made by Miss California USA Carrie Prejean, and had Perez Hilton call her the infamous misogynistic slur â€˜dumb b****â€™ as a result, and as Hilton himself admitted on ABC news after, caused her to lose the nationals,â€ Mandy replied, â€œAnd eventually de-crowned.â€

This touched Mandy, you see, because she was quite opinionative, and if put in Prejeanâ€™s shoes, would have responded in the same way. She could feel Prejeanâ€™s pain. But on her mind, was if asked, would she slip to thinking what other's thought, or only what God thought.

â€œWhilst supporting a cause to prevent anti-gay bullying, Khloe Kardashian noted Hilton was a hypocrite, as her â€˜personal bullyâ€™,â€ Blaire commented, â€œcausing Hilton to rethink his methods, and eventually release a video noting â€˜I am a hypocrite, and I am one of the biggest bullies out thereâ€¦ In the past, I would justify everything as comedy and humorâ€¦ I need to change, and I'm going to, starting today.â€

â€œBut by the grace of God, go I,â€ Mandy commented.

Analogous to gravitational potential energy, since $W=F.d$ (from ), $W=\dfrac{kq_{1}q_{2}}{r^2}.r$, or simplifying, $W=PE=\dfrac{kq_{1}q_{2}}{r}$. Because work has the same units as energy (from ), this is electrical potential energy.

Analogous to gravitational field, electric field explains how particles distort space time via their electrical charge. Electric field is defined as $E=\dfrac{F}{q}$, where $F$ is gravitational force, $q$ is the charge of a test positive charge, and electric field is in the units $N/C$. Since $F=\dfrac{kq_{1}q_{2}}{r^2}$, in-substituting, $E=\dfrac{1}{q}.\dfrac{kq_{1}q_{2}}{r^2}=\dfrac{kq}{r^2}$. Electric field is visualized by forces that would act on a test positive charge particle. Accordingly, field/force lines spring in all directions away from [the center of the] positive charge towards [the center of the] negative charge. This shows that a test positive charge travels away from positive charge towards negative charge.

The electric field produced by two parallel charged plates, would be directed from the positive to the negative plate, at right angles to both plates, so that the charges donâ€™t cross over. Beyond the edges of the plates, the electric fields do curve.

Analogous to gravitational potential energy, electrostatic potential energy is $PE=W=Fd=qEd$.

Voltage (aka electrical potential difference) is the capacity of an electric field to do work on an electric charge, and is defined as energy per unit charge, or $\dfrac{PE}{q}=\dfrac{kq_{1}q_{2}}{r}.\dfrac{1}{q}=\dfrac{kq}{r}$. There is no equivalent for gravity, but if there were, it would be $\dfrac{E}{m}=\dfrac{GMm}{r}.\dfrac{1}{m}=\dfrac{GM}{r}$; or near the surface of the earth, $\dfrac{E}{m}=mgh.\dfrac{1}{m}=gh$. However, this gravitational analogy can be used, to surmise that voltage should also equal the electrostatic equivalent of $gh$, which is $Ed$ respectively, meaning $V=Ed$, and an alternative unit for electric field is thus $V/m$.

Magnetic fields have north and south pole. Electric field lines point from north to south. Like electric charge, like poles repel, and unlike poles attract. Unlike electric charge however, north and south poles cannot be separated.

Current (moving charge) produces a magnetic field that circles the wire. Magnetic field lines are in concentric circles, the direction of which can be determined by the right hand grip rule, which is to put the thumb in the direction of the conventional current, and the fingers show the direction of the magnetic field. The magnetic field is weaker further from the wire.

A charged particle moving in a magnetic field experiences a sideways force, $F=qv\times B=qvb.sin(\theta)$, where $q$ is the electric charge of the particle, $v$ is the velocity of the particle, $B$ is the magnetic field, and $\theta$ is the angle between the particle velocity and magnetic field, known as the Lorentz force. Note that magnetic field is generally illustrated as crosses indicating into the page, and circles indicating out of the page. The Lorentz force is always perpendicular to both particle velocity and magnetic field.

Faradayâ€™s law of induction is that a changing magnetic flux creates an electric field, such that the magnitude of the potential difference created is equal to the rate of change of the magnetic flux. Flux is the strength of a magnetic field in a given area, represented by the proximity of field lines. This induced electric field is unique, in that it is non-conservative, remembering from  that conservative forces can be identified as having a potential energy associated, meaning that induced electric fields donâ€™t have a potential energy associated. For example, if a wire [not carrying a current] is pulled out of a magnetic field, as it is shifting to a non-magnetized area, there is a change in flux. This would thus generate a potential difference, and therefore current in the wire. Lenzâ€™s law is that the induced current creates a magnetic field which opposes the inducing magnetic field. For example, if the [inducing] magnetic field is going into the page, the induced current should create a magnetic field which opposes this. Therefore, the created magnetic field should go out of the page. Placing fingers out of the page [in direction of created magnetic field], and the open palm towards the left of the page [in direction of force], the thumb shows direction of current, which is downward.

 Formative learning activity Maps to RK8 What is electricity? What is magnetism, and how does this relate to magnetism?

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