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Physics 30S Electric Fields

Name:

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Lesson 1: Electric Field Lines Goals:

Define the terms electric field, electric field lines, and lines of force.

Draw an electric field line pattern for an isolated positive point charge or an isolated negative point charge.

Explain what the length of an electric field line, and the direction of an electric field line represent.

Explain what the density of electric field lines represent.

Compare gravitational field lines to electric field lines.

Define the term electric dipole and draw the electric field line pattern for the dipole.

Draw a vector representing the direction and strength of the electric field at any given point in an electric field line pattern.

Draw an electric field line pattern for two charges of the same sign and magnitude.

Draw an electric field line pattern between two oppositely charged parallel plates.

Draw an electric field line pattern for the charge between two plates or near one plate.

Electric Field Lines

Electric field is a region of space around a charge where a positive test charge experiences a force caused by other charges.

The value electric field strength, E⃑⃑ , can be defined to be the ratio of the

electric force, F⃑ , to the charge, q, experiencing the force.

�⃑� = 𝐅 𝐞𝐪

Electric field lines

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Point Charges The electric field lines for a positive charge point away from the charge. The electric field lines for a negative charge point towards the charge. The number of lines is proportional to the charge. Near the charges where the electric field is strongest, the lines are close together. At distances far from the charges, the electric field is weaker so the lines are farther apart. In general, the electric field is strongest in regions where the field lines are closer together.

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Electric Field Lines for Two Charged Point Charges

Electric dipole

In drawing electric field lines, the following important points should be kept in mind.

a) Electric field lines always begin on a positive charge and end on a negative charge, and do not start or stop in the region between.

b) The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.

c) In general, the more lines there are in a given location, the stronger the

field is in that region. For example, there are many lines per unit area close to a charge indicating a strong electric field close to the charge. There are not many field lines farther away from the charge, indicating a weaker field strength in that region.

d) Electric field lines never cross each other. e) The direction of the electric field at any given point is the vector drawn

tangent to the electric field line at that point. The longer the electric field vector, the stronger the electric field.

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Example 1: Several electric field line patterns are shown in the diagrams below. Which of these patterns are incorrect? Explain what is wrong with all incorrect diagrams. Example 2: Erin drew the following electric field lines for a configuration of two charges. What did Erin do wrong? Explain. Example 3: Consider the electric field lines shown in the diagram below. From the diagram, it is apparent that object A is ____ and object B is ____.

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Example 4: Consider the electric field lines drawn below for a configuration of two charges. Several locations are labeled on the diagram. Rank these locations in order of the electric field strength from smallest to largest.

Example 5: Use your understanding of electric field lines to identify the charges on the objects in the following configurations.

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Example 6: Observe the electric field lines below for various configurations. Rank the objects according to which has the greatest magnitude of electric charge, beginning with the smallest charge.

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Practice: Electric Fields

1. What is the purpose of lightning rods on top of tall buildings? 2. Why do you think lightning rods are pointy? 3. How does a Van der Graff generator work? 4. Why did the foil plates fly up when the Van der Graaff generator is

turned on? 5. Which one is easier to charge and stick to the wall, a rubber balloon or

a foil balloon? Explain. 6. Two people of the same height are walking in an open field, one got

struck by a lightning bolt, which is discharged from a cloud the same distance from both the two people, the other one didn’t. Try to explain why the other person got struck.

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7. Explain how lightning is formed. Use diagrams. 8. Sketch the electric fields lines. Use arrows to indicate the direction.

a) - - - - - - b) __________ + + + + + 9. A charge of 125 microC is placed in an electric field where the field

intensity is 3.55 × 105 N/C. What is the magnitude of the force acting on the charge?

10. How many electrons would be needed to neutralize an electroscope

having a charge of +4.5 × 10–12 C?

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11. A deuterium atom contains one proton and one neutron in the nucleus with one electron orbiting at a distance of 5.10 × 10-11 m.

a) Calculate the gravitational force between the nucleus and the electron.

b) Calculate the electrical force between the nucleus and the electron.

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Lesson 2: Calculating Electric Field and Electric Force Goals:

State what a coulomb is.

Calculate the magnitude and direction of the electric force, F⃑ e, acting on

a test charge, q, in an electric field, E⃑⃑ . Compare the direction of the electric field vector and the electric force

vector when the test charge is positive or negative.

Determine the total electric field at a given point when two or more electric fields, in one or two dimensions, act at this point.

Electrostatic force is similar to gravitational force. The relationships are the same, except the agent of force in electrostatic force is charge, whereas in gravitational force, it is mass. Inverse square law also applies to this force. We have seen a unit for charge, the elementary charge (e) which is defined as the amount of charge on a proton (q = e) or electron (q = -e). This is far too small of a unit to be of much use under most circumstances, when large numbers of these particles are involved. The SI unit of charge is in fact the Coulomb abbreviated “C”, named after Charles Coulomb. “Coulomb” can be thought to be the same kind of word as “dozen”, meaning 12. One coulomb is the amount of charge contained in 6.24 × 1018 protons or electrons. Notice then, that a single proton or electron has an amount of charge equal the reciprocal of this number.

1C = 6.24 × 1018 e 1e = 1.6 × 10-19 C = qproton = qelectron (but negative)

Recall Newton’s Law of Universal Gravitation: F⃑ = Gm1m2

r2. It describes the

gravitational force between any two objects with mass. Similarly, two objects with charge experience forces between themselves. The amount of force can be found using Coulomb’s Law.

Coulomb’s Law:

F⃑ = kq1q2

d2

Where k is “Coulomb’s Constant = 9.0 × 109 Nm2/C2 and q1 and q2 are in the SI unit of charge, Coulombs.

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Note the difference in values of the constants. k is very large compared to G. This implies that electrostatic force is much stronger than gravitational force. When using Coulomb’s Law, ignore the sign, positive or negative, of the charge. Then determine the type of force, attractive or repulsive, or direction of the force from the law of charges. Alternatively, use the sign of the charges in the formula, a positive force implies repulsion while a negative force implies attraction. I don’t recommend this method of using signs, just use [attractive] or [repulsive], or the direction of the force. In situations where there are more than two charged objects, you can obtain the net force by considering them in pairs, obtaining the forces, using vectors of course, with Coulomb’s law, and then adding the vectors to obtain a resultant. The Coulomb

In the previous lesson, we defined the value electric field strength, E⃑⃑ , to be

the ratio of the electric force, F⃑ , to the charge, q, experiencing the force.

�⃑� = 𝐅 𝐞𝐪

The electric field, E⃑⃑ , and the electric force, F⃑ e, are both vectors. When determining the electric force, both the magnitude (size), and the direction of the force should be stated.

Example 1: A test charge of +1.0 × 10-6

C experiences a force of 0.050 N. What is the electric field strength?

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Example 2: An object with a charge of 2.0 × 10-4

C creates an electric field.

A test charge of +1.0 × 10-6

C experiences a force of 0.050 N. Calculate the electric field strength.

Example 3: An object with a charge of 2.0 × 10-4

C creates an electric field.

A test charge of +3.5 × 10-6

C experiences a force of 0.10 N. Calculate the electric field strength. Electric Field and Force in One-Dimension Example 4: A test charge of +5.00 C is placed a distance of 2.00 m to the right of the point charge +q. The strength of the electric field produced by this charge is 10.0 N/C at the location of the charge q. Determine the electric force on the test charge.

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Example 5: A test charge of +5.00 C is placed a distance of 2.00 m to the right of the point charge -q. The strength of the electric field produced by this charge is 10.0 N/C at the location of the charge q. Determine the electric force on the test charge.

Example 6: In the diagram below, there are two charges. The positive

charge, q1, on the left creates an electric field, E⃑⃑ 1, of 10.0 N/C to the right at position P. The positive charge on the right, q2, creates and electric field,

E⃑⃑ 2, of 15.0 N/C to the left and position P. Find the total electric field strength and electric force at point P.

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Electric Field and Force in Two-Dimension Example 7: In the next situation, the two electric fields are at right angles relative to each other. The positive charge, q1, creates and electric field of 10.0 N/C north while the charge, q2, creates an electric field of 15.0 N/C east. Find the electric field strength at point P. Example 8: A +4.0 C charge, +q1, is 1.0 m to the left of a 1.0 C charge, +q2.

a) What is the magnitude and direction of the force exerted at the location of the +q2 charge?

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b) The charge +q2 is now removed. The +q1 charge produces an electric field at the location of point P. The magnitude of this electric field is 3.6 × 1010 N/C. Another charge +q3 to the right of point P produces an electric field of magnitude 1.6 × 1010 N/C at point P. What is the total electric field strength at point P and what force would a +5.0 C charge experience at this point?

c) The charge q1 is now removed. It is replaced by a charge -q4. This

charge is directly south of the point P and it produces an electric field of magnitude 2.6 × 1010 N/C. Draw a diagram representing the two electric fields. Then determine the magnitude and direction of the total electric field.

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Practice: Calculating Electric Field and Electric Force

1. Two spheres are separated by a distance of 1.0 m. If each sphere has a charge of 2.0 C, then what force must exist between the spheres?

2. A positive point charge creates and electric field of 5.0 × 104 N/C at a point directly south of the charge. If a test charge of -2.0 C is place at that place, then what is the magnitude and direction of the force on that charge?

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3. A positive point charge, q1, produces a field E⃑⃑ 1, of size 5.0 N/C at a

location “P.” A negative point charge, -q2, produces an electric field E⃑⃑ 2, of size 10.0 N/C at the same location “P.”

a) Determine the magnitude and direction of the total electric field at “P.”

b) If a 4.0 C charge is placed at P, what is the magnitude and the direction of the force on this charge?

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4. A positive point charge, q1, produces a field E⃑⃑ 1, of size 5.0 N/C at a

location P. A negative point charge, -q2, produces an electric field E⃑⃑ 2, of size 10.0 N/C at the same location P.

a) Determine the magnitude and direction of the total electric field at P.

b) If a 4.0 C charge is placed at P, what is the magnitude and the direction of the force on this charge?

Answers:

1. F⃑ = 3.6 × 1010 N

2. F⃑ e = 1.0 × 105 N

3. a) E⃑⃑ = 5.0 N/C West b) F⃑ = 20.0 N West

4. a) E⃑⃑ = 11.2 N/C 27° S of E b) F⃑ = 44 N 27° S of E

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Lesson 3: The Millikan Experiment Goals:

Determine the electric force and the gravitational force on a charged particle and the acceleration of the particle between two charged parallel plates.

Apply the three equations for the motion of an object as discussed in kinematics.

Describe Millikan’s oil drop experiment.

Explain what Millikan attempted to determine in his experiment, and how he determined it.

State the value of an elementary charge in coulombs.

Convert between a charge in coulombs and the number of elementary particles in the charge.

Charged Parallel Plate and Force For a charged particle between two charged plates, the net force on the particle is the sum of the electrical force and the gravitational force on the

particle: 𝐅 net = 𝐅 e + 𝐅 g

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Example 1: The electric field strength between the charged plates is 10.0 N/C, and the object has a charge of +2.00 C and a mass of 4.00 × 10-4 kg. Determine the acceleration of the particle.

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Example 2: In Example 1, we saw that a charge of +2.00 C accelerated upwards at a rate of 5.00 × 104 m/s2. If the particle accelerates upwards for 6.00 μs (6.00 × 10-6 s), determine:

a) The change in velocity and the average velocity.

b) The downward displacement of the charged particle.

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The Millikan Experiment In his experiment, Millikan attempted to determine the answer to two questions.

1. Does there exist in nature a smallest unit of electric charge of which all other units are multiples?

2. If so, what is this elementary charge, and what is its magnitude, in coulombs?

Using a charged oil droplet between two charged plates, Millikan was able to suspend the particle between the two plates. This meant that the sum of the upward electrical force equaled the downward pull of gravity.

𝐅 e = 𝐅 g, and q × �⃑� = m × g. The charge on the charged particle can then be determined by:

𝐪 = 𝐦 × 𝐠

�⃑�

The currently accepted value for the elementary charge is 1.602 177 33 × 10-19 C. Thus the total charge, q, on any object is a whole number multiple, N, of this elementary charge, e.

q = N e The number of elementary charges in this 1C is:

𝐍 = 𝟏

𝟏.𝟔𝟎 × 𝟏𝟎−𝟏𝟗 𝐂/𝐞 = 6.25 × 1018 e

Example 4: A proton whose mass is 1.67 × 10-27

kg is suspended at rest in

a uniform electric field. Take into account gravity and determine E⃑⃑ .

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Example 5: An oil drop weighs 1.9 × 10-15

N. It is suspended in an electric

field intensity of 6.0 × 103 N/C.

a) What is the charge on the drop?

b) How many excess electrons does it carry? Practice: Millikan Problems

1. Most experiments in atomic physics are performed in a vacuum. Describe the effect on the Millikan oil drop experiment of performing it in a vacuum.

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2. A charge, q1 = +5.00 C is placed in an electric field between two

charged plates. The electric field strength is E⃑⃑ = 4.00 N/C. The mass of the charged particle is m = 2.00 × 10-4 kg.

a) Determine the magnitude and direction of the acceleration of the charged particle between the plates.

b) If the particle is released from rest, what will be the displacement of the particle after a time of 8.00 ms (8.00 × 10-3 s)?

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3. How many electrons must be removed from an electrically neutral silver dollar to give it a charge of +2.4 μC?

4. An oil drop, whose mass is found to be 4.95 × 10-15 kg is balanced

between two large horizontal plates with the upper plate positive. The

electric field strength between the plates is E⃑⃑ = 5.10 × 104 N/C. What is the charge on the oil drop, both in coulombs and in elementary charges, and is it an excess or deficit in electrons?

Answers: 2. a) a⃑ = 1.00 × 105 m/s2 downwards b) d = -3.2 m 3. N = 1.5 × 1013 e 4. q = 9.51 × 10-19 C, N = 6 e, there is an excess of electrons

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Extra Practice

1. Two small spheres each having a mass of 0.075 g are suspended by a 35 cm silk threads from the same points. When given equal charges, they separate, the threads making an angle of 23º with each other. What is the electrostatic force acting on the each sphere? Draw a vector diagram.

2. A charge of 125 microC is placed in an electric field where the field intensity is 3.55 × 10 5 N/C. What is the magnitude of the force acting on the charge?

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3. A force of 0.075 N is required to move a charge of 20.0 microC in an electric field between two points 12.0 cm apart. What potential difference exists between the two points?

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