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?
answer
4.5 V
question
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
What is the voltage 3 m away from the charge?
3 V
1 V
9 V
answer
3 V
question
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?
At any point, the electric field is parallel to the equipotential line at that point.
At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of higher voltages.
At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages.
answer
At any point, the electric field is perpendicular to the equipotential line at that point, and it is directed toward lines of lower voltages.
question
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?
The equipotential lines are equally spaced. The distance between each line is the same for all adjacent lines.
The equipotential lines are closer together in regions where the electric field is weaker.
The equipotential lines are closer together in regions where the electric field is stronger.
answer
The equipotential lines are closer together in regions where the electric field is stronger
question
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?
The voltages are positive, but the magnitude increases with increasing distance.
The voltages become negative instead of positive and keep the same magnitudes.
The voltage distribution does not change.
answer
The voltages become negative instead of positive and keep the same magnitudes.
question
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?
Exactly twice the voltage produced by only one of the charges at the same point
Greater than zero, but less than twice the voltage produced by only one of the charges at the same point
Zero
answer
Exactly twice the voltage produced by only one of the charges at the same point
question
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
zero.
negative.
positive.
answer
zero.
question
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?
The electric field strength is greatest where the voltage is the smallest.
The electric field strength is greatest where the equipotential lines are very close to each other.
The electric field strength is greatest where the voltage is the greatest.
answer
The electric field strength is greatest where the equipotential lines are very close to each other.
question
W = 0×(kq2L)
answer
If you calculate W, the amount of work it took to assemble this charge configuration if the point charges were initially infinitely far apart, you will find that the contribution for each charge is proportional to kq^2/L. In the space provided, enter the numeric value that multiplies the above factor, in W.
question
figure a
answer
Which of the following figures depicts a charge configuration that requires less work to assemble than the configuration in the problem introduction? Assume that all charges have the same magnitude q. (Figure 2)
figure a
figure b
figure c
question
Electric field lines always begin at _______ charges (or at infinity) and end at _______ charges (or at infinity). One could also say that the lines we use to represent an electric field indicate the direction in which a _______ test charge would initially move when released from rest. Which of the following fills in the three missing words correctly?
(positive; negative; negative)
(positive; negative; positive)
(negative; positive; negative)
(negative; positive; positive)
answer
(positive; negative; positive)
question
Would a positive test charge released from rest move toward a region of higher or lower electric potential (compared to the electric potential at the point where it is released)?
higher electric potential
lower electric potential
answer
lower electric potential
question
Now imagine that the sign of our test particle is changed from positive to negative, but the electric potential remains the same. Which of the following statements is correct?
The direction of the force will change and it will point to regions of higher potential energy.
The direction of the force will not change and it will point to regions of higher potential energy.
The direction of the force will not change and it will point to regions of lower potential energy.
The direction of the force will change and it will point to regions of lower potential energy.
answer
The direction of the force will change and it will point to regions of lower potential energy.
question
B>A>C=D>F>E
answer
Rank the locations A to F on the basis of the electric potential at each point. Rank positive electric potentials as higher than negative electric potentials.
question
0 J
answer
What is the work done by the electric force to move a 1 C charge from A to B?
question
1 J
answer
What is the work done by the electric force to move a 1 C charge from A to D?
question
greater than the magnitude of the electric field at point B.
answer
The magnitude of the electric field at point C is
greater than the magnitude of the electric field at point B.
less than the magnitude of the electric field at point B.
equal to the magnitude of the electric field at point B.
unknown because the value of the electric potential at point C is unknown.
question
from c to b > from d to a > from c to d > from b to a = from f to e > from c to e
answer
Using the diagram to the left, rank each of the given paths on the basis of the change in electric potential. Rank the largest-magnitude positive change (increase in electric potential) as largest and the largest-magnitude negative change (decrease in electric potential) as smallest.
from b to a
from f to e
from c to d
from c to e
from c to b
from d to a
question
points to the left
answer
A proton is released from Point A. Indicate the direction of the electric force vector acting on the proton.
The electric force vector at Point A:
points upwards
points downwards
points to the left
points to the right
is zero
question
points to the right
answer
An electron is released from Point B. Indicate the direction of the electric force vector acting on the electron.
The electric force vector at Point B
points upwards
points downwards
points to the left
points to the right
is zero
question
The electron released at Point C experiences a greater force.
answer
An electron is released from Point B and a second electron is released from Point C. What can you say about the electric forces experienced by these electrons the instant they are released?
An electron is released from Point B and a second electron is released from Point C. What can you say about the electric forces experienced by these electrons the instant they are released?
The electron released at Point B experiences a greater force.
The electron released at Point C experiences a greater force.
Electrons released from Points B and C would experience equal forces.
The relationship between the two forces cannot be determined.
question
The particle moves to the left through a potential difference of Vb−Va= -2.33 V
answer
The particle, initially at rest, is acted upon only by the electric force and moves from point a to point b along the x axis, increasing its kinetic energy by 1.12×10^−18 J . In what direction and through what potential difference Vb−Va does the particle move?
The particle moves to the left through a potential difference of Vb−Va= 2.33 V .
The particle moves to the left through a potential difference of Vb−Va= -2.33 V
The particle moves to the right through a potential difference of Vb−Va= 2.33 V .
The particle moves to the right through a potential difference of Vb−Va= -2.33 V .
The particle moves to the left through a potential difference of Vb−Va= 23.3 V .
The particle moves to the right through a potential difference of Vb−Va= -23.3 V .
question
VAB=VA−VB=−E(y1−y2)
answer
What is the potential difference VAB=VA−VB between points A and B?
Express your answer in terms of some or all of E, x1, y1, x2, and y2.
question
∞
answer
If the potential at y=±∞ is taken to be zero, what is the value of the potential at a point VA at some positive distance y1 from the surface of the sheet?
∞
−∞
0
−E⋅y1
question
−E⋅y1
answer
Now take the potential to be zero at y=0 instead of at infinity. What is the value of VA at point A some positive distance y1 from the sheet?
∞
−∞
0
−E⋅y1
question
v = 2.5sqrt(kq^2/dm)
answer
The particle with charge q is now released and given a quick push; as a result, it acquires speed v. Eventually, this particle ends up at the center of the original square and is momentarily at rest. If the mass of this particle is m, what was its initial speed v?
Express your answer in terms of q, d, m, and appropriate constants. Use k instead of 1/4πϵ0. The numeric coefficient should be a decimal with three significant figures.
question
no
answer
When the particle with charge q reaches the center of the original square, it is, as stated in the problem, momentarily at rest. Is the particle at equilibrium at that moment?
yes
no
question
1×10^6N/C
answer
What is the magnitude of the electric field between the membranes?
1×10^−15N/C
5×10^−5N/C
9×10^−2N/C
1×10^6N/C
question
4×10^−13N
answer
What is the magnitude of the force on a Ca++ ion between the cell walls?
2×10^−11N
4×10^−12N
2×10^−12N
4×10^−13N
question
1×10^−2V
answer
What is the potential difference between the cell walls?
10V
1×10^7V
1×10^−2V
6×10^−3V
question
Toward the inner wall.
answer
What is the direction of the electric field between the walls?
Toward the inner wall.
Parallel to the walls.
There is no electric field.
Toward the outer wall.
question
3×10^−17J
answer
If released from the inner wall, what would be the kinetic energy of a 3fC charge at the outer wall? 1fC=10^−15C.
3×10^−8J
3×10^−14J
3×10^−17J
3×10^−2J
question
1.5×10^4 m
answer
How far apart would you have to place the poles of a 1.5 V battery to achieve the same electric field?
6.7×10^−9 m
1.5×10^4 m
1.5×10^−2 m
1.5×10^−6 m
question
1.5×10^4 m
answer
How far apart would you have to place the poles of a 1.5 V battery to achieve the same electric field?
6.7×10^−9 m
1.5×10^4 m
1.5×10^−2 m
1.5×10^−6 m
question
W = -0.435 J
answer
A point charge with charge q1 = 3.20 μC is held stationary at the origin. A second point charge with charge q2 = -4.50 μC moves from the point ( 0.170 m , 0) to the point ( 0.270 m , 0.290 m ). How much work W is done by the electric force on the moving point charge?
Express your answer in joules. Use k = 8.99×10^9 N⋅m2/C2 for Coulomb's constant: k=1/4πϵ0.
question
Yes
answer
Is the electric potential energy of a particle with charge q the same at all points on an equipotential surface?
Yes
No
question
Work = 0
answer
What is the work required to move a charge around on an equipotential surface at potential V with constant speed?
question
Work done by the electric field = 0
answer
What is the work done by the electric field on a charge as it moves along an equipotential surface at potential V?
Work done by the electric field =
question
θ = 1.57 rad
answer
The work WE done by the uniform electric field E⃗ in displacing a particle with charge q along the path d⃗ is given by
WE=qE⃗ ⋅d⃗ =q|E⃗ ||d⃗ |cosθ,
where θ is the angle between E⃗ and d⃗ . Since in general, E⃗ is not equal to zero, for points on an equipotential surface, what must θ be for WE to equal 0?
Express your answer in radians.
question
V(x,y,z) = |E|z
answer
Find the electric potential V(x,y,z) at a point X=(x,y,z) inside the capacitor if the origin of the coordinate system O=(0,0,0) is at potential 0.
Express your answer in terms of some or all of the variables E, x, y, and z.
question
Δz = ΔV/E
answer
What is the distance Δz between two surfaces separated by a potential difference ΔV?
Express your answer in terms of E and ΔV.
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