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PHY_10_35_V2_TG_E&G fields.docx
RECOMMENDATIONS
on lesson “Electric and gravitational fields”
Some useful resources for teachers
Problems "Electric field Potential»
Level A
1. Two point charges + 0.1 µC and -0.1 µC are placed in a vacuum at a distance of 5 m from each other. Determine the potential of the electric field at a point located at a distance of 3 m from the first charge and 4 m from the second? (Answer: 75 V)
2. At a distance of 4 m from the solitary positive point charge potential of the electric field is 100 V. Determine the modulus of the field vector at a distance of 5 m from the charge. (Answer: 160 kV/m)
Level В
1. At a distance R from the center of the uncharged metal ball is a point charge q. Determine the potential of the ball.
Level С
1. The electron moved in an accelerating electric field from a point with a potential of 200 To a point with a potential of 300 V. Find the kinetic energy of the electron, the change in its potential energy and the acquired velocity. The initial velocity of the electron is considered to be zero.
Answer: 1.6 · 10 − 5 J, -1.6 · 10 − 5 J, 6 Mm/s.
2. In two points of an equilateral triangle with a side of 0.5 m there are two identical positive charges of 1 µC. Find the potential and intensity of the electric field in the third points of the triangle, as well as in the middle between the charges.
(Answer: 36 kV, 72 kV 62 kV/m; 0)
Teacher might give to students this table of equations:
Example problem with solution:
Let’s imagine a rectangle AQ1BQ2 with sides a = 15 cm and b = 5 cm.
There are two charges Q1 = -5 µC and Q2 = +2 µC placed in vertices Q1 and Q2. How much work have to be done by an electric force to move a charge Q3 = +2 µC diagonaly from the vertex A to the vertex B?
Solution:
The work done by an electric force is proportional to the amount of the moved charge and proportional to the difference of potentials between the starting point and the destination.
Point charge potential depends on amount of the charge and on the distance to the charge. Work done by an electrical force by transferring a charge in an electric field is equal to the difference of potential energies between the starting position A and the final position B
W=EpA−EpB
The electrical field potential is equal to the potential energy of a charge equal to 1 C. We can determine potential energy using the field potential Ep = Q3φ and so we can determine the work:
W=Q3 (φA−φB)W=Q3(φA−φB)
Electrical field potential caused by the first and the second charge in place A is equal to the sum of potentials caused by several charges.
φA=φ1A+φ2A
where φ1A is the potential caused by the first charge and φ2A is the potential caused by the second charge in the place A.
The electrical field potential of the point charge Q in the distance r from the charge is:
and 
QUESTIONS: Electrical Potential Energy
Is the following sentence true or false?
1. A charged object has potential energy by virtue of its location in an electric field.
2. Circle the letter of each statement that is true.
a. N o work is required to push a charged particle against the electric field of a charged body.
b. The electrical potential energy of a charged particle decreases when work is done to push it against the electric field of something else that is charged.
c. The energy a charge has due to its location in an electric field is called electrical potential energy.
d. If a charge with electrical potential energy is released, its electrical potential energy will transform into kinetic energy.
Electric Potential
3. What is electric potential?
____________________________________________________________________________
(Answer: Electric potential is electrical potential energy per charge)
4. Is the following sentence true or false?
Electric potential is not the same as electrical potential energy. __________
(Answer: true)
5. The SI unit of measurement for electric potential is the __________ (answer: Volt)
6. Write an equation that expresses the relationship between volts, joules, and coulombs.
(Answer: 1volt = 1joule/coulomb)
7. What is voltage?
(Answer: a measure of electric potential, expressed in volts)
Additional Multiple choice questions (Average level) Electric Potential Difference Created by Point Charges
9. Two point charges are arranged along the x axis as shown in the figure. At which of the following values of x is the electric potential equal to zero?
Note: At infinity, the electric potential is zero.
(a) +0.05 m (c) +0.40 m (e) +0.71 m
(b) +0.29 m (d) +0.54 m
10. Two point charges are located at two of the vertices of a right triangle, as shown in the figure. If a third charge -2q is brought from infinity and placed at the third vertex, what will its electric potential energy be? Use the following values: a = 0.15 m; b = 0.45 m, and q = 2.0 ´ 10-5 C.
(a) -17 J (d) +8.5 J
(b) -12 J (e) +14 J
(c) -2.8 J
11. A +1.0 mC point charge is moved from point A to B in the
uniform electric field as shown. Which one of the following statements is
necessarily true concerning the potential energy of the point charge?
(a) It increases by 6.0 ´ 10-6J.
(b) It decreases by 6.0 ´ 10-6 J.
(c) It decreases by 9.0 ´ 10-6 J.
(d) It increases by 10.8 ´ 10-6 J.
(d) It decreases by 10.8 ´ 10-6 J.
12. Three point charges –Q, –Q, and +3Q are arranged along a line as shown in the sketch.
What is the electric potential at the point P?
(a) +kQ/R (c) –1.6kQ/R (e) +4.4kQ/R
(b) –2kQ/R (d) +1.6kQ/R
13. If the work required to move a +0.35 C charge from point A to point B is +125 J, what is the potential difference between the two points?
(a) zero volts (c) 88 V (e) 360 V
(b) 44 V (d) 180 V
Questions 14 through 16 pertain to the electrostatic system described below:
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Two point charges are held at the corners of a rectangle as shown in the figure. The lengths of sides of the rectangle are 0.050 m and 0.150 m. Assume that the electric potential is defined to be zero at infinity. |
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14. Determine the electric potential at corner A.
(a) +6.0 ´ 104 V (c) +4.6 ´ 105 V (e) zero volts
(b) –2.4 ´ 105 V (d) –7.8 ´ 105 V
15. What is the potential difference, VB - VA, between corners A and B?
(a) -8.4 ´ 105 V (c) -7.2 ´ 105 V (e) zero volts
(b) -7.8 ´ 105 V (d) -6.0 ´ 105 V
16. What is the electric potential energy of a +3.0 mC charge placed at corner A?
(a) 0.10 J (c) 2.3 J (e) zero joules
(b) 0.18 J (d) 3.6 J
Additional Multiple choice questions (Higher level) Electric Potential Difference Created by Point Charges
Questions 17 through 19 pertain to the situation described below:
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Four point charges are individually brought from infinity and placed at the corners of a square as shown in the figure. Each charge has the identical value +Q. The length of the diagonal of the square is 2a. |
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17. The first two charges are brought from infinity and placed at adjacent corners. What is the electric potential energy of these two charges?
(a) 
(c) 
(e) 
(b) 
(d) 
18. What is the magnitude of the electric field at P, the center of the square?
(a) kQ/a2 (c) 4kQ/a2 (e) zero V/m
(b) 2kQ/a2 (d) kQ/4a2
19. What is the electric potential at P, the center of the square?
(a) kQ/a (c) 4kQ/a (e) zero volts
(b) 2kQ/a (d) kQ/4a
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Questions 20 and 21 refer to the following statement and figure:
P and Q are points within a uniform electric field that are separated by a distance of 0.1 m as shown. The potential difference between P and Q is 50 V. |
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20. Determine the magnitude of this electric field.
(a) 0.5 V/m (c) 50 V/m (e) 5000 V/m
(b) 5.0 V/m (d) 500 V/m
21. How much work is required to move a +1000 mC point charge from P to Q?
(a) 0.02 J (c) 200 J (e) 5000 J
(b) 0.05 J (d) 1000 J
Questions 22 and 23 pertain to the following situation:
Two point charges are separated by 1.00 ´ 10-2 m. One charge is -2.8 ´ 10-8 C; and the other is +2.8 ´ 10-8 C. The points A and B are located 2.5 ´ 10-3 m from the lower and upper point charges as shown.
22. If an electron, which has a charge of 1.60 × 10-19 C, is moved from rest at A to rest at B, what is the change in electric potential energy of the electron?
(a) +4.3 ´ 10-15 J (c) –2.1 ´ 10-14 J (e) zero joules
(b) +5.4 ´ 10-15 J (d) –3.2 ´ 10-14 J
23. If a proton, which has a charge of +1.60 ´ 10–19 C, is moved from rest at A to rest at B, what is change in electrical potential energy of the proton?
(a) +2.1 ´ 10–14 J (c) – 4.3 ´ 10–15 J (e) zero joules
(b) +3.2 ´ 10–14 J (d) – 5.4 ´ 10–15 J
Questions
24 through 26 pertain to the situation described below:
Two charges of opposite sign and equal magnitude Q = 2.0 C are held 2.0 m apart as shown in the figure.
24. Determine the magnitude of the electric field at the point P.
(a) 2.2 ´ 109 V/m (c) 4.4 ´ 108 V/m (e) zero V/m
(b) 5.6 ´ 108 V/m (d) 2.8 ´ 108 V/m
25. Determine the electric potential at the point P.
(a) 1.1 ´ 109 V (c) 4.5 ´ 109 V (e) zero volts
(b) 2.2 ´ 109 V (d) 9.0 ´ 109 V
26. How much work is required to move a 1.0 C charge from infinity to the point P?
(a) zero joules (c) 4.5 ´ 109 J (e) infinity
(b) 2.2 ´ 109 J (d) 9.0 ´ 109 J
Useful resources:
https://www.khanacademy.org/science/electrical-engineering/ee-electrostatics/ee-fields-potential-voltage/a/ee-electric-potential-voltage
https://www.physicsclassroom.com/Class/circuits/u9l1b.cfm
https://www.s-cool.co.uk/a-level/physics/a-comparison-electric-and-gravitational-fields/revise-it/a-comparison-electric-and
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