Chapter 18- Electric Forces and Electric Fields
The flux does not change, as long as the charge remains within the Gaussian surface
A Gaussian surface contains a single charge within it, and as a result an electric flux passes through the surface. Suppose that the charge is then moved to another spot within the Gaussian surface. Does the flux through the surface change?
is the vector sum of the forces exerted by the charges on the rod and the two spheres
A positive charge q0 experiences an electrostatic force (F) due to the...
C. The mass increases if the charge is negative and decreases if it is positive
An electrically neutral object acquires a net electric charge. Which on of the following statements concerning the mass of the object is true? A. The mass does not change B. The mass increases if the charge is positive and decreases if it is negative C. The mass increases if the charge is negative and decreases if it is positive
Electric charge
An intrinsic property of protons and electrons
Spread out
At distances far from the charges, where the electric field is weaker, the lines are more _____________
Move through an object
Electric charge can not only exist on an object but it can also do what?
N*m^2/ C
SI Unit of Electric Flux
In the case of an electric dipole
When are electric field lines curved?
Two unlike materials are rubbed together Objects become "electrified" as surfaces rub against one another
Separation of charge occurs when...
No, because the force of the spring changes direction when the spring is stretched compared to when it's compressed, which the electrostatic force does not have this characteristic
A particle is attached to one end of a horizontal spring, and the other end of the spring is attached to a wall. When the particle is pushed so that the spring is compressed more and more, the particle experiences a greater and greater force from the spring. Similarly, a charged particle experiences a greater and greater force when pushed closer and closer to another particle that is fixed in position and has a charge of the same polarity. Considering this similarity, will the charged particle exhibit simple harmonic motion on being released, as will the particle not the spring?
A. To the left of the positive charge
A positive point charge is located to the left of a negative point charge. When both charges have the same magnitude, there is no place on the line passing through both charges where the net electric field due to the two charges is zero. Suppose, however, that the negative charge has a greater magnitude than the positive charge. On which part of the line, if any, is a place of zero net electric field now located? A. To the left of the positive charge B. Between the two charges C. To the right of the negative charge D. There is no zero place.
D. Its acceleration
A positively charged particle is moving horizontally when it enters the region between the plates of a parallel plate capacitor, (+ plate on top, - plate on bottom). When the particle is within the capacitor, which of the following vectors, if any, are parallel to the electric field lines inside the capacitor? A. The particle's displacement B. Its velocity C. Its linear momentum D. Its acceleration
The electron, because, being less massive, it has a greater acceleration
A proton and an electron are held in place on the x axis. The proton is at x= -d, while the electron is at x= +d. They are released simultaneously, and the only force that affects their motions significantly is the electrostatic force of attraction that each applies to the other. Which particle reaches the origin first?
F=k |q1| |q2| /r^2 This equation gives only the magnitude of the electrostatic force that each point charge exerts on the other; it does not give direction. The electrostatic force is directed along the line joining the charges, and it is attractive if charges have unlike signs and repulsive if the charges have like signs.
Coulomb's law equation
Quanitized
Because any electric charge (q) occurs in integer multiples of elementary, indivisible charges of magnitude (e) electric charge is said to be what?
q= Ne (N) is an integer
Charges of larger magnitude than the charge on an electron or on a proton are built up on an object by adding or removing electrons. Thus, any charge of magnitude (q) is an integer multiple of (e). What is the equation of (q)?
For rod A, the field points perpendicularly away from the rod. For rod B, it points parallel to the rod and is directed from the positive toward the negative half.
Consider two identical, thin, and nonconducting rods, A and B. On rod A, positive charge is spread evenly, so that there is the same amount of charge per unit length at every point. On rod B, positive charge is spread evenly over only the left half, and the same amount of negative charge is spread evenly over the right half. For each rod deduce the direction of the electric field at a point that is located directly above the midpoint of the rod.
Positive charge
The body that loses electrons has an excess of what charge?
Electric field, force
It is the surrounding charges that create an ________ at a given point. Any positive or negative charge placed at the point interacts with the field and, as a result, experiences a __________
Test charge
It is useful to think of q0 as a _________ for determining the extent to which the surrounding charges generate a force.
C. The electric field in A is the same everywhere, but it becomes stronger in B as you move from left to right.
Drawings A and B show two examples of electric field lines. Which (one or more) of the following statements are true, and which (one or more) are false? *Drawing A is 4 parallel straight lines & drawing B is 4 parallel curved lines being more broad on the left and more scrunched on the right* A. In both A and B the electric field is the same everywhere. B. As you move from left to right in each case, the electric field becomes stronger. C. The electric field in A is the same everywhere, but it becomes stronger in B as you move from left to right. D. The electric fields in both A and B could be created by negative charges located somewhere on the left and positive charges somewhere on the right. E. Both A and B arise from a single positive point charge located somewhere on the left.
Law of conservation of electric charge
During any process, the net charge of an isolated system remains constant (is conserved)
Equal, opposite
Each point charge exerts a force on the other. Regardless of whether forces are attractive or repulsive, they are ___________ in magnitude but __________ in direction
Electric field lines
Electric charges create an electric field in the space around them. It is useful to have a kind of "map" that gives the direction and strength of the field at various places. This idea is referred to as what?
Electric field = F/qₒ
Electric field equation
Positive charges, negative charges
Electric field lines are always directed away from ______________ and toward ________________
Perpendicular
Excess negative or positive charge resides on the surface of a conductor at equilibrium under electrostatic conditions. In such a situation, the electric field at any point within the conducting material is zero, and the electric field just outside the surface of the conductor is _______________ to the surface
They end or begin on the induced charges. Consequently, a test charge placed inside the conductor would feel no force due to the presence of the charges on the capacitor. ***In other words, the conductor shields any charge within it from electric fields created outside the conductor. The shielding results from the induced charges on the conductor surface.
Figure 18.29a shows an uncharged, solid, cylindrical conductor at equilibrium in the central region of a parallel plate capacitor. Induced charges on the surface of the cylinder alter the electric field lines of the capacitor. Since an electric field cannot exist within the conductor under these conditions, the electric field lines do not penetrate the cylinder. Instead what happens?
Tangent
For a curved field line, the electric field vector at a point is ___________ to the line at that point
The net charge (Q) enclosed by the surface divided by Eo , the permittivity of free space ΦE = Σ( E cos(θ) ) ΔA= Q/Eₒ
Gauss' law states that the electric flux through a closed surface (a Gaussian surface) is equal to what?
Force
Greater the charge and the closer together they are, the greater the ________
Can do so by contributing to the net external force that acts on the object Newton's second law (F=ma) specifies the acceleration that arises because of the net external force. Any external electric force that acts on an object must be included when determining the net external force to be used in the second law.
How can the electric force alter the motion of an object?
Are also curved Figure 18.26 shows the pattern associated with two positive point charges and reveals that there is an absence of lines in the region between the charges. The absence of lines indicates that the electric field is relatively weak between the charges.
How does the electric field lines in the vicinity of two identical charges?
B. At one of the empty corners
Identical point charges are fixed to diagonally opposite corners of a square. Where does a third point charge experience the greater force? A. At the center of the square B. At one of the empty corners C. The question is unanswerable because the polarities of the charges are not given
Negatively charged object to a positively charged object
If heat is conducted from the hotter end of a metal bar to a cooler end, what would their charges be?
An attractive force
In Coulomb's law the electrostatic force can be either repulsive or attractive, depending on whether or not the charges have the same sign; in contrast, the gravitational force is always what kind of force?
With all of the excess charge on the surface, no further movement of charge occurs & excess positive charge also moves to the surface of a conductor ****In general, at equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor.
In conducting materials such as copper, electric charges move readily in response to the forces that electric fields exert. This property of conducting materials has a major effect on the electric field that can exist within and around them. Suppose that a piece of copper carries a number of excess electrons somewhere within it, as in Figure 18.28a. Each electron would experience a force of repulsion because of the electric field of its neighbors. And, since copper is a conductor, the excess electrons move readily in response to that force. What happens once static equilibrium is established?
Same, same (i.e. field lines between the plates of a parallel plate capacitor are parallel and equally spaced, except near the edges where they bulge outward. The equally spaced, parallel lines indicate that the electric field has the same magnitude and direction at all points in the central region of the capacitor)
In regions where the electric field lines are equally spaced, there is the ____________ number of lines per unit area everywhere, and the electric field has the ____________ strength at all points.
Yes, its direction is the same as the direction of the force on a positive test charge.
Is the electric field a vector? If so, in what and of what same direction does it go?
Repel, attract each other
Like charges _______ and unlike charges _______
Electrical insulators I.e. rubber, many plastics, and wood
Materials that conduct electric charge poorly
Proportional
No matter how many charges are present, the number of lines per unit area passing perpendicularly through a surface is ____________ to the magnitude of the electric field
Indicates that there is no net electric field present within the conductor. In fact, the excess charges arrange themselves on the conductor surface precisely in the manner needed to make the electric field zero within the material. ***Thus, at equilibrium under electrostatic conditions, the electric field is zero at any point within a conducting material.
Now consider the interior of the copper in Figure 18.28b. The interior is electrically neutral, although there are still free electrons that can move under the influence of an electric field. What does the absence of a net movement of these free electrons indicate?
+3.2x10^-13 C on object A and -3.2x10^-13 C on object B
Object A and object B are each electrically neutral. Two million electrons are moved from object A and place on object B. Expressed in coulombs, what is the resulting charge (algebraic sign and magnitude) on object A and on object B?
+1.6x10^-13 C on object A and -3.2x10^-13 C on object B
Object A has a charge of -1.6x10^-13 C, and object B is neutral. Two million electrons are removed from object A and placed on object B. Expressed in coulombs, what is the resulting charge (algebraic sign and magnitude) on object A and on object B?
Lines of force
Since the electric field is the electric force per unit charge, field lines are also called what?
Thermal insulators
Substances that conduct heat poorly are
Thermal conductors I.e. metal
Substances that conduct heat readily are
Electrical conductors I.e metals, copper, aluminum, silver, and gold
Substances the readily conduct electric charge are
First, find the magnitude and direction of the force exerted on q1 by q2 (ignoring q3). Then, determine the force exerted on q1 by q3 (ignoring q2). *The net force on q1 is the vector sum of these forces* (look at figure 18.12 as an example)
Suppose that a third point charge (magnitude |q3| ) is also present. What would be the net force on q1 due to both q2 and q3?
Separate (No electrons or protons are created or destroyed)
Th rubbing process serves to only do what to electrons and protons already present in the materials?
Outward, repulsive
The electric field created by the charge +q is directed radially __________ & experience a/an _________ force
Inward (because the force on a positive test charge is one of attraction, indicating that the electric field points inward)
The electric field created by the charge -q is directed radially __________
Stronger
The electric field is ___________ in regions where the field lines are closer together
Charge, distance
The electrostatic force that stationary charged objects exert on each other depends on the amount of __________ and the __________ between them
The magnitude of the charge i.e. five times as many lines would emerge from a charge as from a +5q charge
The number of field lines is chosen to be proportional to what?
D. They have different magnitudes and different directions.
There is an electric field at point (P). A very small positive charge is placed at this point and experiences a force. Then the positive charge is replaced by a very small negative charge that has a magnitude different from that of the positive charge. Which one of the following statements is true concerning the forces that these charges experience at? A. They are identical. B. They have the same magnitude but different directions. C. They have different magnitudes but the same direction. D. They have different magnitudes and different directions.
(a)No. (b)No.
Three point charges are fixed to the corners of a square, one to a corner, in such a way that the net electric field at the empty corner is zero. Do these charges all have (a) the same sign and (b) the same magnitude (but, possibly, different signs)?
Considering that the sizes of the objects are small compared to the separation distance, we can treat the charges as point charges. Coulomb's law may then be used to find the magnitude of the attractive force, provided that only the magnitudes of the charges are used for the symbols |q1| and |q2| that appear in the law Solution: The magnitude of the force is F=k |q1| |q2| /r^2= (8.99 x 10^9 N*m^2/C^2) (1.0 C)(1.0 C)/ (1.0 x 10^3 m)^2 = 9.0 x 10^3 N
Two objects, whose charges are +1.0 C and , -1.0 C are separated by 1.0 km. Compared to 1.0 km, the sizes of the objects are small. Find the magnitude of the attractive force that either charge exerts on the other.
Negative charge
Usually electrons are transferred, and the body that gains electrons acquires an excess of what charge?
Electric force or electrostatic force
What can alter the motion of an object
The magnitude (F) of the electrostatic force exerted by one point charge (q1) on another point charge (q2) is directly proportional to the magnitudes |q1| and |q2| of the charges and inversely proportional to the square of the distance (r) between them
What does Coulomb's law state?
The idea of flux involves both the electric field and the surface through which it passes. By bringing together the electric field and the surface through which it passes, we will be able to define electric flux and then present Gauss' law.
What does the electric flux idea involve?
That the electric field is greatest in the region between and immediately surrounding the two charges, since the lines are closest together there
What does the pattern of the lines for the dipole indicate?
When an electric dipole consists of two separated point charges that have the same magnitude but opposite signs
What is a dipole moment?
A device that consists of two parallel metal plates, each with area (A). A charge +q is spread uniformly over one plate, while a charge -q is spread uniformly over the other plate. In the region between the plates and away from the edges, the electric field points from the positive plate toward the negative plate and is perpendicular to both.
What is a parallel plate capacitor?
Coulomb (C)
What is the SI unit for measuring the electric charge?
Newton per coulomb (N/C)
What is the SI unit of electric field
The electric field (E) that exists at a point is the electrostatic force (F) experienced by a small test charge (qₒ) placed at that point divided by the charge itself:
What is the definition of the electric field?
Their atomic structure
What is the difference between conductors and insulators?
The product of the magnitude of one of the charges and the distance between the charges
What is the electric field of a dipole proportional to?
The magnitude (E) of the electric field, the area (A) of the surface, and the angle that specifies the direction of the field relative to the normal to the surface ΦE = Σ( E cos(θ) ) ΔA
What is the electric flux (ΦE) through a surface related to?
A proportionality constant: k= 8.99 x 10^9 N*m^2/C^2
What is the k constant in Coulomb's law?
e= 1.60 x 10^-19 C
What is the magnitude of the charge on an electron or a proton
The magnitude of the charge on the proton EXACTLY equals the magnitude of the charge on the electron
What is the relationship between the magnitude of the charge on the proton and the magnitude of the charge on an electron?
The relationship between a charge distribution and the electric field it produces
What relationship does Gauss' law describe?
Conductor
When "free" electrons are able to move readily this is considered to be a/an
Electrically neutral: -The neutrons in the nucleus are electrically neutral particles -Also when the algebraic sum of the positive charge of the nucleus and negative charge of the electrons is zero
When an atom, or any object, carries no net charge, it is said to be what?
Charge distribution
When an electric field is produced by charges that are spread out over a region, rather than by a single point charge, what is this extended collection of charges called?
Insulator
When very few electrons freely move throughout a material this is considered to be a/an
Electric field lines always begin on a positive charge and end on a negative charge and do not start or stop in midspace. Furthermore, the number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
Where do electric field lines always begin and end?
