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Electricity

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Static Electricity• Charge comes in two forms, which Ben Franklin

designated as positive (+) and negative (-).• Charge is quantized.

– The smallest possible stable charge, designated as e, is the magnitude of the charge on 1 electron or 1 proton.

– A proton has charge of e, and an electron has charge of -e.

– e is referred to as the “elementary” charge.

– e = 1.602 x 10-19 coulombs.– The coulomb is the SI unit of charge.

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Sample Problem

• A certain static discharge delivers -0.5 coulombs of electrical charge. How many electrons are in this discharge?

• q = n e

• n = q/e

• n = (-0.5 C) / (-1.602 x 10-19 C)

• n = 3,121,098,626,716,604,245

• OR 3.12 x 10 18

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Sample Problem

• The total charge of a system composed of 1800 particles, all of which are protons or electrons, is 31x10-18 C.

• How many protons are in the system?

• How many electrons are in the system?

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Coulomb’s Law and Electrical Force

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Demo #1

• 1. Demonstrate how you can pick up the tissue without touching it in any way with your body.

• 2. What is occurring on the atomic level that lets you do this?

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The atom

• The atom has positive charge in the nucleus, located in the protons. The positive charge cannot move from the atom unless there is a nuclear reaction.

• The atom has negative charge in the electron cloud on the outside of the atom. Electrons can move from atom to atom without too much difficulty.

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So…

• You charge the balloon by rubbing it on hair or on a sweater, and the balloon becomes negative. How can it pick up a neutral tissue?

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The Electroscope

• The electroscope is• Made from a metal• Or other conductor, • And may be contained • Within a flask.• The vanes are free • to move.

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Demo #21.Rub the plastic rod with

the fur. Bring the rod toward the pole of the electroscope. What happens to the vanes?

2.Explain your observations.

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Demo #3

1.Rub the glass rod with the silk. Bring the rod toward the pole of the electroscope. What happens to the vanes?

2.Explain what you observe.

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Demo #4

1. What happens when you touch the electroscope with the glass rod?

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Electric Force

• Charges exert forces on each other.

• Like charges (two positives or two negatives) repel each other resulting in a repulsive force.

• Opposite charges (a positive and a negative) attract each other, resulting in an attractive force.

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Coulomb’s Law - form 1• Coulomb’s law tells us how the magnitude of the

force between two particles varies with their charge and with the distance between them.

• Coulomb’s law applies directly only to spherically symmetric charges.

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Coulomb’s Law - form 2

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Spherically Symmetric Forces

Newton’s Law of Gravity

FG = Gm1m2

r2

Coulomb’s Law

FE = kq1q2

r2

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Sample Problem

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Sample Problem

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Superposition

• Electrical force, like all forces, is a vector quantity.

• If a charge is subjected to forces from more than one other charge, vector addition must be performed.

• Vector addition to find the resultant vector is sometimes called superposition.

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Gravitational Fields

F = ma

• GmEmm = ma

• (2rE) 2

• a = G m E

• 4rE 2

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The Electric Field

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Why use fields?

• Forces exist only when two or more particles are present.

• Fields exist even if no force is present.

• The field of one particle only can be calculated.

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Field around a + charge

**The arrows in a field

are not vectors, they

are “lines of force”.

**The lines of force

indicate the direction

of the force on a

positive charge

placed in the field.

**Negative charges

experience a force

in the opposite direction.

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Field around a - charge

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Field between charged plates

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Field vectors from field lines

• The electric field at a given point is not the field line itself, but can be determined from the field line.

• The electric field vector is always tangent to the line of force at that point.

• Vectors of any kind are never curved!

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Field Lines and Pathof Moving Charge

• The electric field lines do not represent the path a test charge would travel.

• The electric field lines represent the direction of the electric force on a test particle placed in the field.

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Field Vectors from Field Lines

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Force from an Electric Field

• The force on a charged particle placed in an electric field is easily calculated.

• F = Eq– F: Force (N)– E: Electric Field (N/C)– q: Charge (C)

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Sample Problem

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Sample Problem

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Sample Problem

• A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude of 5400 N/C directed in the +y direction. Find the acceleration.

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For Spherical Electric Fields

• The electric Field surrounding a point charge or a spherical charge can be calculated by: E = k q / r2 where– E: Electric Field (N/C)– k: 8.99 x 109 N m2 / C2

– q: Charge (C)– r: distance from center of charge q (m)

• Remember that k = 1/4

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Principle of Superposition

• When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.

• Again, as with force vectors, this is referred to as superposition.

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Keep in mind…

• Electric field lines are NOT vectors, but may be used to derive the direction of electric field vectors at given points.

• The resulting vector gives the direction of the electric force on a positive charge placed in the field.

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Sample Problem

• A particle bearing -5.0 C is placed at -2.0 cm and a particle bearing 5.0 C is placed at 2.0 cm. What is the field at the origin?

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Sample Problem

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Sample Problem

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Electric Potential Energy

• The energy contained in a configuration of charges.

• Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable.

• Unit: Joule

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Electric Potential Energy

• increases when charges are brought into less favorable configurations.

U>0

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Electric Potential Energy

• decreases when charges are brought into more favorable configurations.

U<0

•

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Electric Potential Energy

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Work and Charge

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Work and Charge

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Electric Potential

• Electric potential is hard to understand, but each to measure.

• We commonly call it “voltage”, and its unit is the Volt.

• 1 V = 1 J / C

• Electric potential is easily related to both the electric potential energy and to the electric field.

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Electrical Potential andPotential Energy

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Electrical Potential andPotential Energy

V = U / q

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Sample Problem

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Electrical Potential in UniformElectric Fields

• The electric potential is related in a simple way to a uniform electric field.

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Sample Problem

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Sample Problem Fr75