Chpt. 22 HW
The electric potential (voltage) at a specific location is equal to the potential energy per unit charge a charged object would have if it were at that location. If the zero point of the voltage is at infinity, the numerical value of the voltage is equal to the numerical value of work done to bring in a unit charge from infinity to that location. Select Show numbers and grid in the green menu, and drag one positive charge to the middle of the screen, right on top of two intersecting bold grid lines. Using the voltage meter, you should find that 1 m away from the charge, the voltage is 9 V. What is the voltage 2 m away from the charge?
4.5V ~Unlike the magnitude of the electric field, the electric potential (voltage) is not proportional to the inverse of the distance squared.
Shown are three separate pairs of point charges. Assume the pairs interact only with each other. Rank the magnitudes of the force between the pairs from largest to smallest. a) -1q<---------2x-------->+36q b) +4q<--------2x--------->+8q c) +2q<-----x---->-2q
A, B, C
If the field strength is E = 9 V/m a distance of 1 m from the charge, what is the field strength E a distance of 3 m from the charge?
E = 1 V/m ~Since E∝1/r2, if the distance is increased by a factor of three, the electric field is decreased by a factor of nine.
In the diagram below, there are three collinear point charges: q1, q2, and q3. The distance between q1 and q2 is the same as that between q2 and q3. You will be asked to rank the Coulomb force on q1 due to q2 and q3. (The figure shows three charges, labeled q 1, q 2, and q 3, on a grid. The charges lie on the same horizontal line at a distance of 3 cells from each other. Charge q 2 is located to the right of charge q 1 and to the left of charge q 3.) PART A Rank the six combinations of electric charges on the basis of the electric force acting on q1. Define forces pointing to the right as positive and forces pointing to the left as negative.
Largest [q1=+1nC, q2=-1nC, q3=-1nC] & [q1=-1nC, q2=+1nC, q3=+1nC] [q1=+1nC, q2=-1nC, q3=+1nC] [q1=+1nC, q2=+1nC, q3=-1nC] Smallest [q1=+1nC, q2=+1nC, q3=+1nC] & [q1=-1nC, q2=-1nC, q3=-1nC]
What is meant by saying that charge is quantized? a) All charged objects have a charge that is an integer multiple of the charge of an electron. b) All objects have a charge that is equal to the charge of the electron. c) All electric charges are fractions of the electron charge with a 1 in the numerator. d) All electric charge is measured in units called "quants."
a) All charged objects have a charge that is an integer multiple of the charge of an electron. ~There is no smaller units of charge (than one electron/proton) observed!
Why are materials such as glass and rubber good insulators? a) Electrons are tightly bound to their atoms, making them poor conductors of heat. b) Electrons are loosely bound to their atoms, making them poor conductors of heat. c) Electrons are tightly bound to their atoms, making them good conductors of heat. d) Electrons are loosely bound to their atoms, making them good conductors of heat.
a) Electrons are tightly bound to their atoms, making them poor conductors of heat. ~The outer electrons belong to particular atoms.
Make a long line of positive charges, similar to that shown in the figure below. Try to place all of the charges centered along a horizontal grid line. Feel free to look at the electric field, as it is interesting Measure the strength of the electric field 1 m directly above the middle as well as 2 m directly above. Does the strength of the electric field decrease as 1 over distance squared (1/r2)? Make a long line of positive charges, similar to that shown in the figure below. Try to place all of the charges centered along a horizontal grid line. Feel free to look at the electric field, as it is interesting. The figure shows many positive point charges that are placed very close to each other forming a long horizontal chain. Measure the strength of the electric field 1 directly above the middle as well as 2 directly above. Does the strength of the electric field decrease as 1 over distance squared (1/r2)? a) No, it decreases less quickly with distance. b) No, it decreases more quickly with distance. c) Yes, it does.
a) No, it decreases less quickly with distance. ~In fact, it turns out that the strength of the electric field decreases roughly as 1/r. So the field 1 m above the midpoint is roughly half the strength at 0.5 m. This is another example showing that a distribution of charges produces an electric field that is very different from that of a single charge.
Using the setup from the first question, imagine that you briefly touch the negatively charged rod to the can (assume that this rod is conducting for the sake of effect). You then hold the two rods at equal distances on either side of the can. What does the can do? a) Rolls toward the positively charged rod b) Does not move c) Rolls away from the positively charged rod
a) Rolls toward the positively charged rod ~The can acquires a net negative charge after being touched, so it is then attracted to the positively charged rod.
Consider the situation in the figure below, where two charged rods are placed a distance d on either side of an aluminum can. What does the can do? a) Stays still b) Rolls to the left c) Rolls to the right
a) Stays still ~ The positively charged rod induces a negative charge on the left side of the can, creating an attractive force between the rod and the can. However, the negatively charged rod induces an equal positive charge on the right side of the can, which creates an attractive force between the can and that rod. The net force acting on the can is zero.
Why are metals good conductors of both heat and electricity? a) The outer shell electrons in metals are free to move from atom to atom. b) The outer shell electrons in metals move with zero resistance, making all metals superconductors. c) The outer shell electrons in metals are tightly bound, making it easy for vibrations to move from one atom to the next. d) The outer shell electrons in atoms vibrate in place and emit electromagnetic radiation that travels throughout the metal.
a) The outer shell electrons in metals are free to move from atom to atom. ~"loose" outer shell e-
Make an electric dipole by replacing one of the positive charges with a negative charge, so the final configuration looks like the figure shown below. The electric field at the midpoint is a) directed to the right. b) directed to the left. c) zero.
a) directed to the right. ~The electric field due to the positive charge is directed to the right, as is the electric field due to the negative charge. So the net electric field, which is the sum of these two fields, is also to the right.
What is the flow of current proportional to? a) voltage difference between the two ends of the wire b) voltage at one end of the wire c) voltages at both ends of the wire
a) voltage difference between the two ends of the wire
The three pairs of metal same-size spheres have different charges on their surfaces, as indicated. Each pair is brought together, allowed to touch, and then separated. Rank from greatest to least the total amount of charge on the pairs of spheres after separation. a) +6 +2 b) +6 -2 c) +6 0
a, c, b ~The total charge on the spheres will remain constant after they touch. Initially, A has 8 (6+2) units of charge, B has 4(6+-2) and C has 6(6+0) units of charge. This total will not change. A>C>B
How does a semiconductor differ from a conductor or an insulator? a) A semiconductor has exactly half the resistance of an insulator and twice the resistance of a conductor. b) A semiconductor is neither a good conductor nor a good insulator - it has a middle range of resistivity. c) A semiconductor has exactly half the resistance of a conductor and twice the resistance of an insulator. d) A semiconductor is a good conductor of electric current but a poor conductor of heat.
b) A semiconductor is neither a good conductor nor a good insulator - it has a middle range of resistivity. ~fair insulator in pure crystalline form, excellent conductor when e- added or removed
How does the charge of one electron compare to that of another electron? How does it compare with the charge of a proton? How do the masses of protons and electrons compare? a) All electrons and protons have exactly the same charge. A proton has 1800 times the mass of an electron. b) All electrons have the same charge. Electron charge is equal and opposite to the proton charge. A proton has 1800 times the mass of an electron. c) All electrons and protons have exactly the same charge and mass. d) All electrons have the same charge. Electron charge is equal and opposite to the proton charge. A electron has 1800 times the mass of a proton.
b) All electrons have the same charge. Electron charge is equal and opposite to the proton charge. A proton has 1800 times the mass of an electron.
Another way to study voltage and its relationship to electric field is by producing equipotential lines. Just like every point on a contour line has the same elevation in a topographical map, every point on an equipotential line has the same voltage. Click plot on the voltage tool to produce an equipotential line. Produce many equipotential lines by clicking plot as you move the tool around. You should produce a graph that looks similar to the one shown below. Place several E-Field Sensors at a few points on different equipotential lines, and look at the relationship between the electric field and the equipotential lines. Which statement is true? a) At any point, the electric field is parallel to the equipotential line at that point. b) At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages. c) At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages.
b) At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages. ~All points on an equipotential line have the same voltage; thus, no work would be done in moving a test charge along an equipotential line. No work is done because the electric field, and thus the force on the test charge, is perpendicular to the displacement of the test charge being moved along the equipotential line.
Now, remove the negative charge, and drag two positive charges, placing them 1 m apart, as shown below. What is the voltage at the midpoint of the two charges? a) Greater than zero, but less than twice the voltage produced by only one of the charges at the same point b) Exactly twice the voltage produced by only one of the charges at the same point c) Zero
b) Exactly twice the voltage produced by only one of the charges at the same point ~Because voltage is a scalar quantity, there are no vector components with opposite directions canceling out, as for electric fields. The voltage is simply the sum of the voltages due to each of the individual charges. Since both charges are positive, the voltage due to each charge (at all locations) is positive.
What is meant by conservation of charge? a) The amount of charge in every nucleus is the same. b) Net charge cannot be created or destroyed. c) All electrons have the same electric charge. d) Whenever an electron is created, an equal and oppositely charged proton is also created.
b) Net charge cannot be created or destroyed.
Make a small dipole by bringing the two charges very close to each other, where they are barely touching. The midpoint of the two charges should still be on one of the grid point intersections (see figure below). Measure the strength of the electric field 0.5 m directly above the midpoint as well as 1 m directly above. Does the strength of the electric field decrease as 1 over distance squared (1/r2)? a) No, it decreases less quickly with distance. b) No, it decreases more quickly with distance. c) Yes, it does.
b) No, it decreases more quickly with distance. ~In fact, it turns out that the strength of the electric field decreases roughly as 1/r3! So the field 1 m above the midpoint is roughly eight times weaker than at 0.5 m above the midpoint. The important lesson here is that, in general, a distribution of charges produces an electric field that is very different from that of a single charge.
Remove the positive charge by dragging it back to the basket, and drag a negative charge (blue) toward the middle of the screen. Determine how the electric field is different from that of the positive charge. Which statement best describes the differences in the electric field due to a negative charge as compared to a positive charge? a) Nothing changes; the electric field remains directed radially outward, and the electric field strength doesnât change. b) The electric field changes direction (now points radially inward), but the electric field strength does not change. c) The electric field changes direction (now points radially inward), and the magnitude of the electric field decreases at all locations.
b) The electric field changes direction (now points radially inward), but the electric field strength does not change. ~The electric field is now directed toward the negative charge, but the field strength doesnât change. The electric field of a point charge is given by E⃗ =(kQ/r2)r^. Because of the sign of the charge, the field produced by a negative charge is directed opposite to that of a positive charge but the magnitude of the field is the same.
Now, remove the negative charge, and drag two positive charges, placing them 1 m apart, as shown below Letâs look at the resulting electric field due to both charges. Recall that the electric field is a vector, so the net electric field is the vector sum of the electric fields due to each of the two charges. Where is the magnitude of the electric field roughly equal to zero (other than very far away from the charges)? a) Now, remove the negative charge, and drag two positive charges, placing them 1 apart, as shown below. The figure shows two positive point charges placed on the same horizontal line on a grid, at the distance of ten sides of the grid cells from each other. Letâs look at the resulting electric field due to both charges. Recall that the electric field is a vector, so the net electric field is the vector sum of the electric fields due to each of the two charges. Where is the magnitude of the electric field roughly equal to zero (other than very far away from the charges)? a) The electric field is nonzero everywhere on the screen. b) The electric field is roughly zero near the midpoint of the two charges. c) The electric field is zero at any location along a vertical line going through the point directly between the two charges.
b) The electric field is roughly zero near the midpoint of the two charges. ~Directly between the two charges, the electric fields produced by each charge are equal in magnitude and point in opposite directions, so the two vectors add up to zero.
Make several equipotential lines similar to the figure below. Try to have the equipotential lines equally spaced in voltage. Then, use an E-Field Sensor to measure the electric field at a few points while looking at the relationship between the electric field and the equipotential lines. Which of the following statements is true? a) The electric field strength is greatest where the voltage is the greatest. b) The electric field strength is greatest where the equipotential lines are very close to each other. c) The electric field strength is greatest where the voltage is the smallest.
b) The electric field strength is greatest where the equipotential lines are very close to each other. ~Locations where the voltage is changing steeply are locations with a strong electric field. The magnitude of the electric field is equal to the rate the voltage is changing with distance. Mathematically, this idea is conveyed by |Es|=dV/ds, where Es is the component of the electric field in the direction of a small displacement ds. (As you learned earlier, the electric field is directed in the direction where the voltage decreases.)
Equipotential lines are usually shown in a manner similar to topographical contour lines, in which the difference in the value of consecutive lines is constant. Clear the equipotential lines using the Clear button on the voltage tool. Place the first equipotential line 1 m away from the charge. It should have a value of roughly 9 V. Now, produce several additional equipotential lines, increasing and decreasing by an interval of 3 V (e.g., one with 12 V, one with 15 V, and one with 6 V). Don't worry about getting these exact values. You can be off by a few tenths of a volt. Which statement best describes the distribution of the equipotential lines? a) The equipotential lines are closer together in regions where the electric field is weaker. b) The equipotential lines are closer together in regions where the electric field is stronger. c) The equipotential lines are equally spaced. The distance between each line is the same for all adjacent lines
b) The equipotential lines are closer together in regions where the electric field is stronger. ~Near the positive charge, where the electric field is strong, the voltage lines are close to each other. Farther from the charge, the electric field is weaker and the lines are farther apart.
What happens to a lamp when you take both ends of the wire connected to it and hold them to the same side of the 12-volt terminal of battery, and why? a) The lamp lights up because voltage is applied to it. b) The lamp does not light up because there is no voltage difference applied across it. c) The lamp does not light up, because there is no voltage applied to it. d) The lamp lights up because a voltage difference is applied to it.
b) The lamp does not light up because there is no voltage difference applied across it.
What happens when you have a voltage difference between the two ends of the lamp, and why? a) The lamp lights up because voltage is applied to it. b) The lamp lights up because there is a voltage difference applied to it. c) The lamp does not light up, because there is no voltage applied to it.
b) The lamp lights up because there is a voltage difference applied to it.
Now, remove the positive charge by dragging it back to the basket, and drag one negative charge toward the middle of the screen. Determine how the voltage is different from that of the positive charge. How does the voltage differ from that of the positive charge? a) The voltage distribution does not change. b) The voltages become negative instead of positive and keep the same magnitudes. c) The voltages are positive, but the magnitude increases with increasing distance.
b) The voltages become negative instead of positive and keep the same magnitudes. ~The voltage is still inversely proportional to the distance from the charge, but the voltage is negative everywhere rather than positive.
Select Show E-field and grid in the green menu. Drag one positive charge and place it near the middle of the screen, right on top of two intersecting bold grid lines. You should see something similar to the figure below. The electric field produced by the positive charge a) wraps circularly around the positive charge. b) is directed radially away from the charge at all locations near the charge. c) is directed radially toward the charge at all locations near the charge.
b) is directed radially away from the charge at all locations near the charge. ~This means that another positive charge, if placed near the original charge, would experience a force directed radially away from the original charge.
Consider a point 0.5 m above the midpoint of the two charges. As you can verify by removing one of the positive charges, the electric field due to only one of the positive charges is about 18 V/m. What is the magnitude of the total electric field due to both charges at this location? a) zero b) 36 V/m c) 25 V/m
c) 25 V/m ~Notice that this number is less than twice the magnitude of the field due to each charge. This occurs because the horizontal components of the electric field due to each charge exactly cancel out (add to zero). Only the vertical components of the fields add together.
What is the voltage 3 away from the charge? a) 1 V b) 9 V c) 3 V
c) 3 V ~Based on this result, and the previous question, the electric potential (voltage) is inversely proportional to the distance r from the charge: V∝1/r. Recall that the magnitude of the electric field E∝1/r2.
As in the video, we apply a charge +Q to the half-shell that carries the electroscope. This time, we also apply a charge -Q to the other half-shell. When we bring the two halves together, we observe that the electroscope discharges, just as in the video. What does the electroscope needle do when you separate the two half-shells again? a) It deflects more than it did at the end of the video. b) It deflects less than it did at the end of the video. c) It does not deflect at all. d) It deflects the same amount as at end of the video.
c) It does not deflect at all. ~The spherical surface has zero net charge after the two halves are brought together. The two half-spheres remain electrically neutral after they are separated.
What is the most common net charge of an atom? a) Negative b) Positive c) Neutral d) Dipole
c) Neutral ~Atoms usually have as many electrons as protons, so the atom has a zero net charge.
Now, consider the situation shown in the figure below. What does the can do? a) Rolls to the right b) Rolls to the left c) Stays still
c) Stays still ~The polarization force is always attractive, so the can does not move.
How does the flow of current differ in a superconductor compared with the flow in ordinary conductors? a) In a superconductor, the current flows in the opposite direction to current in a conductor. b) When current flows in a superconductor, it's temperature drops toward absolute zero. A normal conductor gets warmer when current flows. c) Superconductors have infinite conductivity (current flows forever), whereas ordinary conductors have a small resistance to the flow of electric charge. d) When a battery is connected to a superconductor, the current grows exponentially. In a conductor, the current is constant.
c) Superconductors have infinite conductivity (current flows forever), whereas ordinary conductors have a small resistance to the flow of electric charge.
A pipe is filled with water, and there is a piston at each end. If you apply unequal pressures at the two pistons, which way will the water flow in the pipe? a) Water will flow from the piston with the lower pressure to the piston with the higher pressure. b) Water will not flow in either direction. c) Water will flow from the piston with the higher pressure to the piston with the lower pressure.
c) Water will flow from the piston with the higher pressure to the piston with the lower pressure.
What is the magnitude of the electric field 1 m away from the positive charge compared to the magnitude of the electric field 2 m away? The magnitude of the electric field 1 m away from the positive charge is a) one-quarter b) one-half c) four times d) two times e) equal to the magnitude of the electric field 2 m away.
c) four times ~The magnitude of the field decreases more quickly than the inverse of the distance from the charge. The magnitude of the electric field is proportional to the inverse of the distance squared (E∝1/r2, where r is the distance from the charge). You should verify this by looking at the field strength 3 or 4 meters away. This is consistent with Coulombâs law, which states that the magnitude of the force between two charged particles is F=kQ1Q2/r2.
Now, make an electric dipole by replacing one of the positive charges with a negative charge, so the final configuration looks like the figure shown below. What is the voltage at the midpoint of the dipole? The voltage at the midpoint of the dipole is a) negative. b) positive. c) zero.
c) zero. ~Because the voltage due to the negative charge has the opposite sign of the voltage due to the positive charge at the midpoint, the net voltage is zero. The electric field, however, is not zero here!
A positive charge is kept (fixed) at the center inside a fixed spherical neutral conducting shell. The positive charge is equal to roughly 16 of the smaller charges shown on the surfaces of the spherical shell. Which of the pictures best represents the charge distribution on the inner and outer walls of the shell? a) 1 b) 2 c) 3 d) 4 e) 5
d) 4 ~ + signs evenly distributed outside, - signs evenly distributed on the inside)
Why does the gravitational force between Earth and Moon predominate over electrical forces? a) The gravitational force between two protons is billions of times stronger than the electrical force. b) Gravitational forces grow exponentially with the number of particles, while electrical forces simply add. c) The electrical force gets smaller more quickly with distance than the inverse square gravitational force. d) The electric force between Earth and Moon cancels out because they have an equal number of positive and negative charges
d) The electric force between Earth and Moon cancels out because they have an equal number of positive and negative charges
Which part of an atom is positively charged, and which part is negatively charged? a) Atoms are made entirely of neutral particles. b) The nucleus is negatively charged and the electron cloud is positively charged. c) The core is positively charged, the mesosphere is neutrally charged, and the exosphere is negatively charged. d) The nucleus is positively charged and the electron cloud is negatively charged.
d) The nucleus is positively charged and the electron cloud is negatively charged.
An electric field is basically _________. a) a source of voltage b) the same as a gravitational field c) an invisible force d) a vector quantity
d) a vector quantity
Now, let's look at how the distance from the charge affects the magnitude of the electric field. Select Show numbers on the green menu, and then click and drag one of the orange E-Field Sensors. You will see the magnitude of the electric field given in units of V/m (volts per meter, which is the same as newtons per coulomb). Place the E-Field Sensor 1 m away from the positive charge (1 m is two bold grid lines away if going in a horizontal or vertical direction), and look at the resulting field strength. Consider the locations to the right, left, above, and below the positive charge, all 1 m away. For these four locations, the magnitude of the electric field is a) greatest to the right of the charge. b) greatest below the charge. c) greatest above the charge. d) the same. e) greatest to the left of the charge.
d) the same. ~This result implies that the strength of the electric field due to one point charge depends solely on the distance away from the charge. Mathematically, we say the electric field is spherically symmetric.