1 Electrostatics NCSSM - PH. 354 March, 2006 Gabriela Stefan.

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Electrostatics

NCSSM - PH. 354

March, 2006

Gabriela Stefan

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Objectives

After studying this chapter, you should: • know the different types of electric charge and the magnitude of the

smallest available charge.

• know the difference between insulators and conductors.

• be able to use Coulomb's law and apply it to situations involving many charges.

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Charge

http://www.dl.ket.org/physics/companion/ThePC/compan/estat/pos2pith.htm• there are two kinds of charge, positive and negative • like charges repel, unlike charges attract • positive charge comes from losing electrons; negative charge comes from gaining

electrons • charge is quantized, meaning that charge comes in integer multiples of the

elementary charge e

q = n e

• q is the symbol used to represent charge, while n is a positive or negative integer, and e is the electronic charge, 1.60 x 10-19 Coulombs.

• charge is conserved in isolated systems

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Friction

Charging two different materials using a wool cloth• http://www.regentsprep.org/Regents/physics/phys03/aeleclab/chargstp.htm

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Conduction• An electroscope is a device used to detect the presence of charge and it's relative

amount.  One method of charging the electroscope is by conduction or contact.  This means that a charged object must actually touch the electroscope and transfer charge too.  If the electroscope returns to normal after being touched by the charged object then it is quite possible that the charged object is so weakly charged that it is not willing to share its excess charge with the electroscope.

When charging something by contact it is important to note the following properties:• The objects must actually touch and transfer some electrons.• The objects become charged alike.• The original charged object becomes less charged because it actually lost some

charge.  Therefore, there is a limit to how many times it could be used to charge something without being recharged.

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Inducing a Positive Charge on a Sphere • The induction process is characterized by

the following general features:• A charged object is needed to charge an

object by induction. Yet there is never any contact made between the charged object and the object being charged.

• Only conductors can be charged by the induction process. The process relies on the fact that a charged object can force or induce the movement of electrons about the material being charged.

• The object being charged ends up with a charge which is the opposite of the object being used to charge it.

• A ground must be used to create the charge on the object. The ground allows for electron movement into or out of the object being charged.

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Charging a Two Sphere System by Induction

• http://www.physicsclassroom.com/mmedia/estatics/itsn.html

The induction process is characterized by the following general features:

A charged object is needed to charge an object by induction. Yet there is never any contact made

between the charged object and the object being charged.

Only conductors can be charged by the induction process. The process relies on the fact that a charged object can force or induce the movement of electrons

about the material being charged. The object being charged ends up with a charge which is the opposite of the object being used to charge it. A ground must be used to create the charge on the

object. The ground allows for electron movement into or out of the object being charged.

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Electroscope

When the positively-charged electroscope is touched, its charge becomes grounded (or neutralized). This is depicted in the animation to the right. The grounding process involves a transfer of electrons between the charged electroscope and the conducting object to which it is touched. When a positively-charged electroscope is touched, electrons enter the electroscope from the ground. Being positively charged, the electroscope attracts some electrons from the conducting material (in this case, a person). The negatively-charged electrons enter the electroscope and neutralize the positive charge. As the electroscope loses its charge, the needle relaxes back to its naturally upright position.

http://www3.ltu.edu/~s_schneider/physlets/main/electroscope.shtml

1. Grounding a Positively charged Electroscope

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2. Grounding a Negatively Charged Electroscope

• When the negatively-charged electroscope is touched, its charge becomes grounded (or neutralized). This is depicted in the animation to the right. The grounding process involves a transfer of electrons between the charged electroscope and the conducting object to which it is touched. When a negatively-charged electroscope is touched, electrons leave the electroscope to the ground. Since electrons repel other electrons, their tendency is to spread out as far as possible through any conductor. To excess electrons, the farther away that they can be from one another, the better. When touched by a larger conducting material (in this case, a person), the electrons have an opportunity to spread out even further by using the vast space of the ground. The excess electrons leave the electroscope, thus neutralizing its overall charge. As the electroscope loses its charge, the needle relaxes back to its naturally upright position.

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Electrophorus

• Johannes Wilcke invented and then Alessandro Volta perfected the electrophorus over two hundred years ago. This device was quickly adopted by scientists throughout the world because it filled the need for a reliable and easy-to-use source of charge and voltage for experimental researches in electrostatics. A hand-held electrophorus can produce significant amounts of charge conveniently and repeatedly. It is operated by first frictionally charging a flat insulating plate called a "cake". In Volta's day, the cake was made of shellac/resin mixtures or a carnauba wax film deposited on glass. Nowadays, excellent substitutes are available. TeflonTM, though a bit expensive, is a good choice because it is an excellent insulator, charges readily, and is easy to clean and maintain. The electrophorus is ideal for generating energetic capacitive sparks.

• The electrophorus consists of a conductive (metal) electrode with an insulating handle and an insulating plate. Provision for grounding the electrode must be provided. First, the insulating plate is triboelectrically charged by rubbing it with a dry cloth. The resulting surface charge, while itself immobile, makes it possible to charge the electrode by induction. http://www.ece.rochester.edu:8080/~jones/jethberel/elphorus/electrophorus_iexplorer.htm

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Coulomb‘s Law

• The Parallel between Gravity and Electrostatics

http://physics.bu.edu/~duffy/semester2/c02_gravity.html• Java Applets

http://www.tamuk.edu/math/scott/physlets/Doc/Applets.htm

•   Third-law force pair between charges - Coulomb's Law   

http://physics.bu.edu/~duffy/semester2/c01_magnitude.html

• Force vs Distance

http://physics.bu.edu/~duffy/semester2/c01_coulomb.html

• Coulomb’s Law with multiple discrete charges

http://www3.ltu.edu/~s_schneider/physlets/main/coulomb.shtml

• Dr. Hershfield University of Florida

http://www.phys.ufl.edu/~phy3054/elecstat/Welcome.html

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Inverse Square Laws

Coulomb’s Law Newton’s Law

Similarities:Both the forces are directly proportional to the product of the interacting

commodities (mass and charge) Both the forces are inversely proportional to the square of the distance of

separation Differences:

The Coulombian force can be attractive or repulsive while the gravitational force is attractive only

The magnitude of the Coulombian force depends upon the medium separating the charges while the gravitational force is independent of the

medium  

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Principle of Superposition

• Electrical forces obey what is known as the principle of superposition.

• The electrical force acting on a test charge at position vector r is simply the vector sum of all of the Coulomb law forces from each of the N charges taken in isolation. In other words, the electrical force exerted by the j th charge (say) on the test charge is the same as if all the other charges were not there.

• Remember that force is a vector, so when more than one charge exerts a force on another charge, the net force on that charge is the vector sum of the individual forces.

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Practice Problems

• 1. Suppose that two point charges, each with a charge of +1.00 Coulomb are separated by a distance of 1.00 meter. Determine the magnitude of the electrical force of repulsion between them. (Felect = 9.0 x 109 N)

• 2. Two balloons are charged with an identical quantity and type of charge: -6.25 nC. They are held apart at a separation distance of 61.7 cm. Determine magnitude of the electrical force of repulsion between them. (Felect = 9.23 x 10-7 N)

• 3. Two balloons with charges of +3.37 µC and -8.21 µC attract each other with a force of 0.0626 Newtons. Determine the separation distance between the two balloons. (d = +1.99 m)

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Problems 4. The Q in Coulomb's law equation stands for the _____.• a. mass of a charged object• b. # of excess electrons on the object• c. the current of a charged object• d. the distance between charged objects• e. charge of a charged object

5. The symbol d in Coulomb's law equation represents the distance from ___.

• a. A to B b. A to D c. B to C d. B to D e. C to D f. A to G g. B to F h. C to E

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Problems

• 6. Determine the electrical force of attraction between two balloons with separate charges of +3.5 x 10-8 C and -2.9 x 10-8 C when separated a distance of 0.65 m.

 • 7. Determine the electrical force of attraction between two balloons

with opposite charges but the same quantity of charge of 6.0 x 10-7 C when separated a distance of 0.50 m.

  • 8. A balloon has been rubbed with wool to give it a charge of -1.0 x

10-6 C. A plastic rod with a charge of +4.0 x 10-6 C localized at a given position is held a distance of 50.0 cm above the balloon. Determine the electrical force of attraction between the rod and the balloon.

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Problems

• 9. A balloon with a charge of 4.0 µC is held a distance of 0.70 m from a second balloon having the same charge. Calculate the magnitude of the repulsive force.

  • 10. At what distance of separation must two 1.00-microCoulomb

charges be positioned in order for the repulsive force between them to be equivalent to the weight of a 1.00-kg mass?

• 11. A sphere with charge 6.0 µC is located near two other charged spheres. A – 3.0 µC sphere is located 4.00 cm to the right and a 1.5 µC sphere is located 3.00 cm directly underneath. Determine the net force on the 6.00 µC sphere.

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Problems

• 12. How many coulombs of charge are on the electrons in a nickel? Use the following method to find the answer.

• A. Find the number of atoms in a nickel. A nickel has a mass of about 5g. Each mole (6.02 x 10+ 23 atoms) has a mass of about 58g.

• B. Find the number of electrons in the coin. A nickel is 75% Cu and 25% Ni, so each atom on average has 28.75 electrons.

• C. Find how many coulombs of charge are on the electrons.

• P3 page 478 Problems: 30, 31, 32, 33, 34

• 13. A 0.90-gram balloon with a charge of -75 nC is located a distance of 12 cm above a plastic golf tube which has a charge of -83 nC. How could one apply Newton's laws to determine the acceleration of the balloon at this instant? (a = 5.5 m/s/s, down)

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Problems• 14. A positively-charged object with a charge of +85 nC is being used to

balance the downward force of gravity on a 1.8-gram balloon which has a charge of -63 nC. How high above the balloon must the object be held in order to balance the balloon? (NOTE: 1 nC = 1 x 10 -9 C) (r=0.155 meters )

• 15. Balloon A and Balloon B are charged in a like manner by rubbing with animal fur. Each acquires an excess of 25 trillion electrons. If the mass of the balloons is 1 gram, then how far below Balloon B must Balloon A be held in order to levitate Balloon B? Assume the balloons act as point charges. (r = 3.83 meters )

• 16. Two 1.2-gram balloons are suspended from light strings attached to the ceiling at the same point. The net charge on the balloons is -540 nC. The balloons are distanced 68.2 cm apart when at equilibrium. Determine the length of the string. (r = 78.8 cm )

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Problems

• 17. ZINGER: Three charges are placed along the X-axis. Charge A is a +18 nC charge placed at the origin. Charge B is a -27 nC charge placed at the 60 cm location. Where along the axis (at what x-coordinate?) must positively-charged C be placed in order to be at equilibrium? (x = -267 cm)

• 18*. Two 1.1-gram balloons are suspended from 2.0-meter long strings and hung from the ceiling. They are then rubbed ten times with animal fur to impart an identical charge Q to each balloon. The balloons repel each other and each string is observed to make an angle of 15 degrees with the vertical. Determine the electric force of repulsion, the charge on each balloon (assumed to be identical), and the quantity of electrons transferred to each balloon as a result of 10 rubs with animal fur.(Felect = 0.00289 N) (Q = 5.87 x 10-7 C (negative) ) (# excess electrons = 3.67 x 1012 electrons )

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Problems

• 19. Four charges are arranged in a square with sides of length 2.5 cm. The two charges in the top right and bottom left corners are +3.0 x 10 -6 C. The charges in the other two corners are -3.0 x 10-6 C. What is the net force exerted on the charge in the top right corner by the other three charges? (F net = 118 N)

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Problems

• The notation FBA is used to denote the force of B on A. 

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Problems

FBD (Free Body Diagrams)