# Template:Physeq2

Please do not use this template. Instead go to Physics equations/Equations or a subpage and transclude from there.

- This template focuses on equations used in second semester physics.

## Contents

- 1 SampleName
- 2 18 Electric charge and field
- 3 19 Electric Potential and Electric Field
- 4 20 Electric Current, Resistance, and Ohm's Law
- 5 21 Circuits, Bioelectricity, and DC Instruments
- 6 22 Magnetism
- 7 23 Electromagnetic Induction, AC Circuits, and Electrical Technologies
- 8 24 Electromagnetic Waves
- 9 25 Geometric Optics
- 10 26 Vision and Optical Instruments
- 11 27 Wave Optics
- 12 28 Special Relativity
- 13 29 Introduction to Quantum Physics
- 14 30 Atomic Physics
- 15 31 Radioactivity and Nuclear Physics
- 16 32 Medical Applications of Nuclear Physics
- 17 33 Particle Physics
- 18 34 Frontiers of Physics
- 19 Light: Refraction, ray optics, diffraction, and polarization
- 20 Field theories

#### SampleName[edit]

- Foo

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## 18 Electric charge and field[edit]

#### ScalarElectricField[edit]

- is Coulomb's law for the force between two charged particles separated by a distance r: k
_{e}≈8.987×10^{9}N·m²·C^{−2}, and ε_{0}≈8.854×10^{−12}F·m^{−1}. - is the electric force on a "test charge", q, where is the
*magnitude*of the electric field situated a distance*r*from a charge, Q.

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#### VectorElectricField[edit]

Consider a collection of particles of charge , located at points (called *source points*), the electric field at (called the *field point*) is:

- is the electric field at the field point, , due to point charges at the source points, , and points from source points to the field point.

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#### VectorElectricFieldCALCULUS[edit]

- is the electric field due to distributed charge, where , and denote
**linear**,**surface**, and**volume**density (or**charge density**), respectively. Here, k=1/4πε_{o}.

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## 19 Electric Potential and Electric Field[edit]

#### DefineElectricPotential[edit]

- is the potential energy of a particle of charge, q, in the presence of an electric potential V.
- is a unit of energy, defined as the work associated with moving one electron through a potential difference of one volt.
- (measured in Volts) is the variation in electric potential as one moves through an electric field . The angle between the field and the displacement is θ. The electric potential, V, decreases as one moves parallel to the electric field.
- describes the electric potential if the field is not uniform.
- due to a set of charges at where .

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#### Capacitors[edit]

- is the (equal and opposite) charge on the two terminals of a capacitor of capicitance, C, that has a voltage drop, V, across the two terminals.
- is the capacitance of a parallel plate capacitor with surface area, A, and plate separation, d. This formula is valid only in the limit that d
^{2}/A vanishes. If a dielectric is between the plates, then ε>ε_{0}≈ 8.85 × 10^{−12}due to shielding of the applied electric field by dielectric polarization effects. - is the energy stored in a capacitor.
- is the
*energy density*(energy per unit volume, or Joules per cubic meter) of an electric field.

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#### FieldTheoryCALCULUS[edit]

- in the limit that the Riemann sum becomes an integral.
- where is the del operator.

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#### VolumeSurfaceLineElements[edit]

*Cartesian coordinates (x, y, z)*:

- is a volume element
- and and are area elements of the form
- is a line element.

*Cylindrical coordinates (ρ, φ, z):*

- is a volume element

- if azimuthal symmetry holds.

- and
**are surface elements in cylindrical coordinates.** - and and are line elements in cylindrical coordinates.

*Spherical coordinates (r, θ, φ): Spherical symmetry holds when nothing depends on the angular variables.*

- is the simplest line element in spherical coordinates.
- defines the
**solid angle**. The solid angle of a sphere is 4π**steradians**. - is the volume element of a spherical shell of radius
*r*and thickness*dr*.

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#### GradStokesDivThms[edit]

- is the gradient theorem.

- is the divergence theorem

Here, Ω is a (3-dimensional) volume and ∂Ω is the boundary of the volume, which is a (two-dimensional) surface. Also a surface is Σ, which, if open, has the boundary ∂Σ, which is a (one-dimensional) curve.

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#### GausslawSimple[edit]

- is Gauss's law for the surface integral of the electric field over
*any*closed surface, and is the total charge inside that surface. The vacuum permittivity is ε_{0}≈ 8.85 × 10^{−12}.

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#### Gausslaw[edit]

- is Gauss's law for the surface integral of the electric field over
*any*closed surface, and is the total charge inside that surface. - is a useful variant if the medium is dielectric.
=ε**D**is the electric displacement field. The**E****permittivity**, ε = (1+χ)ε_{0}, where ε_{0}≈ 8.85 × 10^{−12}, and the electric susceptibility, χ, represents the degree to which the medium can be polarized by an electric field. The free charge, Q_{free}, represents all charges except those represented by the susceptibility, χ.

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## 20 Electric Current, Resistance, and Ohm's Law[edit]

#### OhmsLawResistivity[edit]

- defines the electric current as the rate at which charge flows past a given point on a wire. The direction of the current matches the flow of positive charge (which is opposite the flow of electrons if electrons are the carriers.)
- is Ohm's Law relating current, I, and resistance, R, to the difference in voltage, V, between the terminals. The resistance, R, is positive in virtually all cases, and if R > 0, the current flows from larger to smaller voltage. Any device or substance that obeys this linear relation between I and V is called ohmic.
- relates the density (n), the charge(q), and the average drift velocity (v
_{drift}) of the carriers. The area (A) is measured by imagining a cut across the wire oriented such that the drift velocity is perpendicular to the surface of the (imaginary) cut. - expresses the resistance of a sample of ohmic material with a length (L) and area (A). The 'resistivity', ρ ("row"), is an intensive property of matter.

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#### FundamentalDefinitions[edit]

- Power is energy/time, measured in joules/second or J/s. Often called P (never p). It is measured in watts (W)
- Current is charge/time, measured in coulombs/second or C/s. Often called I or i. It is measured in amps or ampheres (A)
- Electric potential (or voltage) is energy/charge, measured in joules/coulomb or J/C. Often called V (sometimes E,
*emf*, ). It is measured in volts (V) - Resistance is voltage/current , measured in volts/amp or V/A. Often called R (sometimes r, Z) It is measured in Ohms (Ω).
- is the power dissipated as current flows through a resistor

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## 21 Circuits, Bioelectricity, and DC Instruments[edit]

#### MiscCircuits[edit]

- is the effective resistance for resistors in series.
- is the effective resistanc vor resistors in parallel.

- and are Kirchoff's Laws
^{[1]} - for the voltage divider shown.

**Simple RC circuit**^{[2]}The figure to the right depicts a capacitor being charged by an ideal voltage source. If, at t=0, the switch is thrown to the other side, the capacitor will discharge, with the voltage,*V*, undergoing exponential decay:

where *V _{0}* is the capacitor voltage at time

*t = 0*(when the switch was closed). The time required for the voltage to fall to is called the RC time constant and is given by

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## 22 Magnetism[edit]

##### VectorMagneticForce[edit]

- is the force on a particle with charge q moving at velocity
with in the presence of a magnetic field**v**. The angle between velocity and magnetic field is θ and the force is perpeduclar to both velocity and magnetic field by the right hand rule.**B** - expresses this result as a cross product.
- is the force a straight wire segment of length carrying a current, I.
- expresses thus sum over many segments to model a wire.
- CALCULUS: In the limit that we have the integral, .

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##### DefineMagneticFieldVector[edit]

- is the contribution to the field due to a short segment of length carrying a current I, where the displacement vector
points from the source point to the field point.**r**

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##### DefineMagneticFieldVectorCALCULUS[edit]

- and the volume integral , where is current density.
- is Ampere's law relating a closed integral involving magnetic field to the total current enclosed by that path.

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##### DefineMagneticFieldScalar[edit]

- is the magnetic field at a distance
*r*from an infinitely long wire carrying a current, where μ_{0}= 4π × 10^{−7}N A. This field points azimuthally around the wire in a direction defined by the right hand rule. Application of the force law on a current element, we have - is the force between two long wires of length separated by a short distance . The currents are I
_{1}and I_{2}, with the force being attractive if the currents are flowing in the same direction.

Call with {{Physeq2|transcludesection=DefineMagneticFieldScalar}}These equations are exact in that they serve to define both μ_{0} as well a the ampere.

#### CyclotronMotion[edit]

For a particle moving perpendicular to **B**, we have cyclotron motion. Recall that for uniform circular motion, the acceleration is *a=v ^{2}/r*, where

*r*is the radius. Since sin θ =1, Newton's second law of motion (F=ma) yields,

Since, sin θ =0, for motion parallel to a magnetic field, particles in a uniform magnetic field move in spirals at a radius which is determined by the perpendicular component of the velocity:

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#### HallEffect[edit]

The Hall effect occurs when the magnetic field, velocity, and electric field are mutually perpendicular. In this case, the electric and magnetic forces are aligned, and can cancel if *qE=qvB* (since sinθ = 1). Since both terms are porportional to charge, q, the appropriate ratio of electric to magnetic field for null net force depends only on velocity:

- ,

where we have used the fact that voltage (i.e. emf or potential) is related to the electric field and a displacement parallel to that field: *ΔV = -E Δs cosθ*

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## 23 Electromagnetic Induction, AC Circuits, and Electrical Technologies[edit]

#### FaradayLaw[edit]

- is a consequence of the magnetic force law as seen in the reference frame of a moving charged object, where
*E*is the electric field perceived by an observer moving at velocity*v*in the presence of a magnetic vield,*B*. Also written as,*E = vBsinθ*, this can be used to derive Faraday's law of induction. (Here, θ is the angle between the velocity and the magnetic field.) - is the magnetic flux, where θ is the angle between the magnetic field and the
**normal**to a surface of area,**A**. - is
**Faraday's law**where*t*is time and*N*is the number of turns. The minus sign reminds us that the emf, or, acts as a "voltage" that opposes the change in the magnetic field or flux.**electromotive force**

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## 24 Electromagnetic Waves[edit]

#### DisplacementCurrent[edit]

- is called the displacement current because it replaces the current density when using Ampère's circuital law to calculate the line integral of the magnetic field around a closed loop.

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## 25 Geometric Optics[edit]

##### ThinLensEquation[edit]

relates the focal length *f* of the lens, the image distance *S _{1}*, and the object distance

*S*. The figure depicts the situation for which (S

_{2}_{1}, S

_{2}, f) are all positive: (1)The lens is converging (convex); (2) The real image is to the right of the lens; and (3) the object is to the left of the lens. If the lens is diverging (concave), then f < 0. If the image is to the left of the lens (virtual image), then

*S*.

_{2}< 0Call with {{Physeq2|transcludesection=ThinLensEquation}}

## 26 Vision and Optical Instruments[edit]

## 27 Wave Optics[edit]

#### InterferenceDiffraction[edit]

- where describes the constructive interference associated with two slits in the Fraunhoffer (far field) approximation.

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#### Beats[edit]

- where is the high frequency carrier and is the slowly varying envelope. Here,

- and . Consequently, the beat frequency heard when two tones of frequency and is .

- models the addition of two waves of equal amplitude but different path length, .

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## 28 Special Relativity[edit]

## 29 Introduction to Quantum Physics[edit]

## 30 Atomic Physics[edit]

## 31 Radioactivity and Nuclear Physics[edit]

## 32 Medical Applications of Nuclear Physics[edit]

## 33 Particle Physics[edit]

## 34 Frontiers of Physics[edit]

## Light: Refraction, ray optics, diffraction, and polarization[edit]

## Field theories[edit]

### Define g, E, B (static case)[edit]

- ↑ https //en.wikipedia.org/w/index.php?title=Kirchhoff%27s_circuit_laws&oldid=579357795
- ↑ From https://en.wikipedia.org/w/index.php?title=RC_circuit&oldid=598786790