Introduction

Electric charge.

Electricity and Magnetism are both observable phenomena originated from interactions of elementary charged particles. An Interaction can be viewed as a feel of presence of other object cause by some of its properties. Thus a mass of a particle t makes it "feel" gravity, and attract another masses. "Charge" is a special property of a particle and it's magnitude contribute the to the magnitude of interactions between charged particles, while sign of charge responsible for either attraction ( between particles of opposite charge) or repulsion ( between charges of same sign) The most important elementary charged particles for our "visible" word are electrons and quarks. Electrons are very light particles that carry a unit of negative charge (-1). Quarks have a fractional charge ($\pm \frac{1}{3}, \pm \frac{2}{3}$) and in groups of 3 form protons (charge+1) and neutrons(charge 0). Protons and neutrons form a positively charged nuclei, nuclei attract and keep negatively charged electrons and form atoms (charge 0). Am atoms is nuclei surrounded by a cloud of electrons, and as it has no charge the number of electrons in it's cloud is exactly equal to the number of protons in its nuclei. Different atoms combines in molecules of materials we observe by sharing their electron clouds. Simple.

The Force and The Field of Force.

Force and Field quantitatively describe the magnitude and direction of interactions between objects in space. We can think that the force is acting on a probe object due to field of force created by other object(s). A probe object itself is a source of field that can be used to find force between it and other objects. Specifically, a force field is a vector field $\vec {F}$, where $\vec{F} (\vec{x})$ is the force that a particle would feel if it were at the point $\vec {x}$. Electric and Gravitational fields are created correspondingly by masses and charges.

Example: As we know two massive objects attract each other with force $\sim \frac{ m_{1} \times m_{2} }{r^2}$. We can think that mass m_1 creates a gravitational field $\vec{G}_{grav}$ distributed in space proportionally to $\frac {m_1}{r^2}$. And then the gravitational force acting on ${m_2} $ is $\vec{F}_{grav} =m_2 \times \vec{G}_{grav}$. Similary, a positive charge $q_1$ creates electric force field which is proportional to $\frac{ q_1 } {r^2}}$, defined as $\vec {E}$ . The force acting on a charge $q_2$ is now $\vec{F_{el}} =q_2 \times \vec{E}$.

Magnetic field

Now, how charged particles connected to Magnetism? The thing is that a charged object not only creates a force field just because it has charge, but also when it moves. A charge *Q* moving along a straight line at speed \vec{v} creates a vector force field $\vec{B}$ around this line with the magnitude inverse proportional to the distance from the line and directed along tangent to the circles of same magnitude (Bio-Savar-Laplas law for infinite wire conductor) : $\vec{B} \sim \frac{ \vec{I} \times \vec{r} }{r^2}$, where $I \equiv dQ/dt$ denotes electric current ( here we have a *vector product* of current and distance to the wire) This second force field is know as a Magnetic field. Magnetic field is also created by changes of electrical field and also by particles that carry a magnetic moment $\mu$ (an internal property of a particle that is equivalent to a magnetic field that produces by a wire loop of area $S$ and current $I$, $m = I \times S$ ) . Magnetism thus is a label for the force field created by moving charged objects, or objects with a magnetic moment (magnets), or changing electric field. And because magnetic field is not produced by a special "magnetic" charge but is derivative phenomenon of electric charge the complete theory of electric and magnetic interactions was simply called Electromagnetism.

Units of measurement (SI system)

• electric current , I - Amper , 1 A == current that case two parallel wire conductors of 1m length attracts with force of 2x10^{-7} N (Newtons) at 1m distance between them
• difference in electric potential between two points in space, "напряжение", 1 V = 1 W/ 1 A = 1 J/ 1C between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points.[2] It is also equal to the potential difference between two parallel, infinite planes spaced 1 meter apart that create an electric field of 1 newton per coulomb. Additionally, it is the potential difference between two points that will impart one joule of energy per coulomb of charge that passes through it
• electric charge, Q - Coulomb, "кулон" - 1 C = 1 A (Amper) * 1 (c)
• electric field, E - 1 N/C ( from $E = F/q$ or 1 V/m ( from $E = \partial \phi / d$ )
• magnetic field, B - 1 T(Tesla) = 1N /(A *m) (from $\vec{F} = q* \vec{v} \times \vec{B} $, Lorent's force)

Maxwell equations

Maxwell equations summarize the observations of electromagnetic phenomena and allow calculate electric and magnetic fields from distributions of electric charge and current. Below is the differential form of Maxwell equations in vacuum, where $\varepsilon_0$ and $\mu_{0}$ correspondingly electric and magnetic constants ( also called "electric and magnetic "проницаемости" of vacuum, $\varepsilon_0 = \frac{1}{\mu_{0} c^2} $

• $\mathbf{\nabla \cdot \vec{E} =\frac{\rho}{\varepsilon_{0}} }$, "Divergence of the electric field in some point is equal to the density $\rho= dQ/dV$ of electric charge in this point" (1)
• $\mathbf{\nabla \cdot \vec{B} = 0} $, "Divergence of the magnetic field is zero ( no magnetic charge)" (2)
• $\mathbf{\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} }$ , " Alternating magnetic field creates "vihrevoe" electric field" (3)
• $\mathbf{\nabla \times \vec{B} = \mu_{0} \vec{j} + \varepsilon_{0}\frac{\partial \vec{E}}{\partial t}}$, "Alternating electric field and current of density $\vec {j} = d\vec{I}/dS$ create "vihrevoe" magnetic field", (4)

Ch 10. Electrical Forces and Fields in Physics

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Lesson 1 - Electric Charge and Force: Definition, Repulsion & Attraction Take Quiz

Lesson 2 - Electric Force Fields and the Significance of Arrow Direction & Spacing Take Quiz

Lesson 3 - Coulomb's Law: Variables Affecting the Force Between Two Charged Particles Take Quiz

Lesson 4 - Insulators and Conductors: Examples, Definitions & Qualities Take Quiz

Lesson 5 - Gauss' Law: Definition & Examples Take Quiz

Go to chapter Electrical Forces and Fields in Physics Practice test: Electrical Forces and Fields in Physics

Ch 11. Potential and Capacitance in Physics

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Lesson 1 - Electric Field & the Movement of Charge Take Quiz

Lesson 2 - Voltage Sources: Energy Conversion and Examples Take Quiz

Lesson 3 - Electric Potential Energy: Definition & Formula Take Quiz

Lesson 4 - Electric Potential: Charge Collections and Volt Unit Take Quiz

Lesson 5 - Finding the Electric Potential Difference Between Two Points Take Quiz

Lesson 6 - What is Capacitance? - Definition, Equation & Examples Take Quiz

Lesson 7 - Capacitance: Units & Formula Take Quiz

Lesson 8 - Fixed & Variable Capacitors: Parts & Types Take Quiz

Lesson 9 - Capacitors: Construction, Charging & Discharging Take Quiz

Lesson 10 - Ohm's Law: Definition & Relationship Between Voltage, Current & Resistance Take Quiz

Lesson 11 - The Potential of a Sphere Take Quiz

Lesson 12 - The Potential of a Cylinder Take Quiz

Practice test: Potential and Capacitance in Physics

Ch 12. Direct Current Circuits in Physics

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Lesson 1 - What is Electric Current? - Definition, Unit & Types Take Quiz

Lesson 2 - Electrical Resistance: Definition, Unit & Variables Take Quiz

Lesson 3 - Electric Circuit Fundamentals: Components & Types Take Quiz

Lesson 4 - Series Circuits: Definition & Concepts Take Quiz

Lesson 5 - Parallel Circuits: Definition & Concepts Take Quiz

Lesson 6 - Applying Kirchhoff's Rules: Examples & Problems Take Quiz

Lesson 7 - Resistor-Capacitor (RC) Circuits: Definition & Explanation Take Quiz

Go to chapter Direct Current Circuits in Physics Practice test: Direct Current Circuits in Physics

Ch 13. Magnetism in Physics

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Lesson 1 - Magnetic Force: Definition, Poles & Dipoles Take Quiz

Lesson 2 - What is a Magnetic Field? Take Quiz

Lesson 3 - How Magnetic Fields Are Created Take Quiz

Lesson 4 - How Magnetic Forces Affect Moving Charges Take Quiz

Lesson 5 - Electromagnetic Induction: Definition & Variables that Affect Induction Take Quiz

Lesson 6 - Electromagnetic Induction: Conductor to Conductor & Transformers Take Quiz

Lesson 7 - Electric Motors & Generators: Converting Between Electrical and Mechanical Energy Take Quiz

Lesson 8 - Faraday's Law of Electromagnetic Induction: Equation and Application Take Quiz

Lesson 9 - The Biot-Savart Law: Definition & Examples Take Quiz

Lesson 10 - Ampere's Law: Definition & Examples Take Quiz

Lesson 11 - Maxwell's Equations: Definition & Application Take Quiz

Go to chapter Magnetism in Physics Practice test: Magnetism in Physics