Physics 4th

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Electrical Potential Energy

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Electrical Potential Energy

When a test charge is placed in an electric field, it experiences a force

The work done within the charge field system by the electric field on the charge through an infinitesimal displacement is 

As this work is done by the field, the change in potential energy is 

For a finite displacement of the charge from A to B,


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Electric Potential

  • The potential energy per unit charge, is the electrical potential 

  • The electrical potential is 

  • The potential is a scalar quantity. Because energy is a scalar

  • As a charged particle moves in an electric field, 

  • The equations for electric potential between two points A and B can be simplified if the electric field is uniform

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Volt

The units of the electric potential

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Downward

when the electric field is directed __ point B at a lower potential than point A

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loses potential energy

When a positive test charge moves from A to B, the charge-field system

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Electric field lines

always point in the direction of decreasing electric potential.

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Equipotentials

  • Point B is at a lower potential than point A

  • Points A and C are at the same potential.

  • All points in a plane perpendicular to a uniform electric field are at the same electric potential.

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Equipotential surface

  • is given to any surface consisting of a continuous distribution of points having the same electric potential.

  • must always be perpendicular to the electric field lines passing through them.

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Voltage

Electric potential is also called applied to a device or across a device is the same as the potential difference across the device.

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Electron-Volts

  • Another unit of energy that is commonly used in atomic and nuclear physics is the electron-volt

  • One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude (an electron or a proton) is moved through a potential difference of 1 volt. 

  • 1 eV = 1.60 x 10-19 J

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Parallel-plate capacitor

This configuration of plates is called a parallel-plate capacitor

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Potential and Point Charges

The potential difference between points A and B will be

The electric potential is independent of the path between points and It is customary to choose a reference potential of 

Then the potential due to a point charge at some point is 

The electric potential due to several point charges


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Outward

An isolated positive point charge produces a field directed radially__

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Positive

If the two charges are the same sign, U is ___ and work must be done to bring the charges together.

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Negative

If the two charges have opposite signs, U is ___ and work is done to keep the charges apart

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More than two charges

If there are ___, then find U for each pair of charges and add them.

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Equipotential lines

are the dashed blue lines

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E and V for a Point Charge

  • The electric field lines are the brown lines.

  • The electric field is radial.

  • Er =-dV/dr

  • The equipotential lines are everywhere perpendicular to the field lines.

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Capacitors

- are devices that store electric charge. 

- Examples of where capacitors are used include:

  • radio receivers

  • filters in power supplies 

  • to eliminate sparking in automobile ignition systems 

  • energy-storing devices in electronic flashes

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Makeup of a capacitor

  • A capacitor consists of two conductors. 

  • These conductors are called plates.

  • When the conductor is charged, the plates carry charges of equal magnitude and opposite directions.

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Capacitance

(C)  of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the potential difference between the conductors.

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SI unit of capacitance

  • farad (F). The farad is a large unit, typically you will see microfarads (mF) and picofarads (pF)

  • The capacitance will always be a positive quantity

  • The capacitance of a given capacitor is constant.

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Capacitance Parallel Plates

Each plate is connected to a terminal of the battery (source of potential difference).

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A

is the area of each plate, and the area of each plate is equal

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Q

is the charge on each plate, equal with opposite signs. 

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Dielectric

is a nonconducting material that, when placed between the plates of a capacitor, increases the capacitance and Increase the maximum operating voltage. Dielectrics include rubber, glass, and waxed paper

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Tubular

  • Metallic foil may be interlaced with thin sheets of paraffin-impregnated paper or Mylar.

The layers are rolled into a cylinder to form a small package for the capacitor.

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Oil Filled

  • Common for high-voltage capacitors A number of interwoven metallic plates are immersed in silicon oil.

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Electrolytic

Used to store large amounts of charge at relatively low voltages

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Electrolyte

  • A solution that conducts electricity by virtue of motion of ions contained in the solution.

  • When a voltage is applied between the foil and the electrolyte, a thin layer of metal oxide is formed on the foil. 

  • This layer serves as a dielectric.

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Electric current (/)

is the rate of flow of charge through some region of space.

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Current density

  • Is the current density of a conductor. It is defined as the current per unit area.

  • J = I / A

  • J is uniform and A is perpendicular to the direction of the current.

  • J has SI units of A/m^2

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Conductivity

  • A current density and an electric field are established in a conductor whenever a potential difference is maintained across the conductor.

  • The constant of proportionality, o, is called the conductivity of the conductor

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Ohm’s Law

  • states that for many materials, the ratio of the current density to the electric field is a constant o that is independent of the electric field producing the current.

  • Mathematically, J=oE or V=IR

  • Materials that obey this law are said to be ohmic. 

  • Most metals obey this law

  • Materials that do not obey this law are said to be nonohmic.

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Resistance of conductor

  • The quantity R = /oA is called the resistance of the conductor. 

  • Defined as the ratio of the potential difference across a conductor to the current in the conductor:

SI units of resistance are ohms  

Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor.

Most electric circuits use circuit elements called resistors to control the current in the various parts of the circuit.

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P

is the resistivity at some reference temperature T

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T

is usually taken to be 20° c

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a

  • is the temperature coefficient of resistivity

SI units of a are °C-1

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Resistors

  • Most electric circuits use circuit elements called resistors to control the current in the various parts of the circuit.

  • Can be built into integrated circuit chips.

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Values of resistors are normally indicated by colored bands.

  • The first two bands give the first two digits in the resistance value.

  • The third band represents the power of ten for the multiplier band.

  • The last band is the tolerance.

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Resistors in Series

For a series combination of resistors, the currents are the same in all the resistors

The potential difference will divide among the resistors

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Consequence of Conservation of Energy

The equivalent resistance has the same effect on the circuit as the original combination of resistors.

If one device in the series circuit creates an open circuit, all

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Superconductors

  • A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, Tc.

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Tc

is called the critical temperature.

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The value of Tc is sensitive to

  • chemical composition

  • pressure

  • molecular structure

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Power

  • is the rate at which the energy is delivered to the resistor.

  • given by the equation P = I AV

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