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Physics Help >> Physics Homework Help >> Electric Potential Energy

 

ELECTRIC POTENTIAL ENERGY


 

 

Charged particles have energy due to their positions. A group of positively charged particles squeezed tightly together has just such energy. When released they will fly apart, converting the potential energy into kinetic. Two charges, Q and q separated by a distance r have electric potential energy

U = kQq/r where k = 9 x 109 . When r = infinity, U = 0.

Electric potential energy is the work required to bring charges from infinite separation to separation r.

ELECTRIC POTENTIAL
The charge , Q, causes every other charge, q, to have electric potential energy. Q is called the source charge as it is considered to be the cause of the electric potential energy, while q is called a test charge.

A common definition for electric potential is the work done per unit charge moving a test charge from infinity to a point in an electric field. The units are J/C, or volts (V). The electric potential is a vector quantity. The direction electric potential is by definition the direction of the force on a positively charged object: the potential points away from a positive source charge, and toward a negative source charge.

V = U/q

Therefore, U = Vq

That is, the work done on every coulomb of charge of a test charge to bring it from infinity to at a distance r away from the source of the field is

U = kQ/r

The work done moving a charge, q, from one point with potential V1 to another point with potential V2 in the field is

U = q(V2 -V1)

PROBLEMS
1. Two protons move toward each other at 4 X 106 m/s. How close together do they get?

 


Three charges are placed at the charge of an isoceles triangle.2. Three charges, q1 = 4 x 10-6 C, q2 = -2 x 10-6 C, and q3 = 5 x 10-6 C are placed at the corners of an isosceles triangle with sides 0.30 m. What is the potential energy of the system?

 

 

 

 

 

 

 

3. What is the speed of an electron that has been accelerated from rest through a potential difference of 80.0 kV?


A positive charge is moved from place to place in an electric field produced by parallel plates.4. A positive charge of magnitude, q, is placed at position, A, between two charged parallel plates as shown to the left. The parallel plates have a potential difference of ΔV and are separated by a distance, d.

State the increase or decrease in potential energy of the particle when it is moved from (a) A to B; (b) B to C; (c) C to D; (d) D to E

 

 

A charged particle is injected into an electric field between two charged parallel plates.

5.
a. A particle with a charge of 3 X 10-8 C and 2 X 10-5 J of kinetic energy enters the region between two charged parallel plates as shown to the left. How far into the region will the particle travel?

b. If an electron were released from rest next to the negative plate, with what speed would it strike the positive plate?

 

 

 

6. Through what potential difference would an electron have to be accelerated to give it a deBroglie wavelength of 10-10 m? (velocity electron<<velocity light).

 

7. A particle (charge 7.5 x 10-6 C)is released from rest at a point on the x-axis, x = 0.1 m. It begins to move

 

due to the presence of a 2.0 x 10-6 C charge which remains fixed at the origin. What is the kinetic energy of

 

the particle at the instant it passes the point x = 1.0 m?

 

8. A charge of uniform density (0.80 nC/m) is distributed along the x-axis from the origin to the point x = 0.1m.

 

What is the electric potential (relative to zero at infinity) at a point x=0.18m, on the a-axis?

 

9. Three equal point charges, each with a charge of 1.50 µC, are placed at the corners of an equilateral

 

triangle whose sides have a length of 0.200 m. What is the potential energy of the system? (Take as zero the

 

potential energy of the three charges when they are infinitely far apart.) Use 8.85×10-12 for the perceptivity of

 

free space.

 

10. Two protons and an alpha particle are held at rest at the corners of an equilateral triangle whose side

 

length is 9.20×10-10 . The particles are released and move apart. What is their total energy when they are

far apart? Use 1.60×10-19 C for the magnitude of the charge on an electron.

 

11. An electron moving to the right at 1.0% the speed of light enters a uniform electric field parallel to its direction of motion. If the electron is to be brought to rest in the space of 4.0 cm, (a) what direction is required for the electric field, and (b) what is the strength of the field?

 

12. A charge of 2.75 µC is held fixed at the origin. A second charge of 2.75 µC is released from rest at the position (1.15 m, 0.490 m) . a) If the mass of the second charge is 3.30 g, what is its speed when it moves infinitely far from the origin? in m/s b.)At what distance from the origin does the 2.75 µC charge attain half the speed it will have at infinity?

 

13. What is the charge of q if location A is 2.40 m from the charge, location B is 4.5m away from the charge, and VB-VA=45V?

 

14. Two point charges of magnitude 4 nC and 5nC are seperated by 39 cm. The Coulomb constant is 8.98755 x 109. What is the potential difference between a point inifinitely far away and a point midway between the charges? Answer in units of V.

 

15. An electron that is initially 53 cm away from a proton is displaced to another point. The Coulomb constant is 8.98755 x 109 Nm2/C2 and the acceleration of gravitiy is 9.8 m/s2. If the change in electric potential energy as a result of this movement is 3 x 10-28 J, what is the final distance between the electron and the proton? Answer in units of m.

 

16. To move a charged particle through an electric potential difference of 2.0x10-6 V requires 4.8x10-6 J of energy. What is the magnitude of the charge?



ANSWERS
1. When no outside forces such as friction acts on an system, the total energy of the system is constant. That is, the sum of kinetic, and potential energies at one point is the same as at any other time.

Etotal = (0.5)mv2 + U is unchanging if no work is done on the system.

At infinite separation and since the system contains 2 protons, the total energy is

Etotal = 2(0.5)mv2 + kQq/r


= 2(0.5)(1.67 X 10-27 kg)(4 X 106 m/s)2 + 0

= 2.67 X 10-14 J

At their closest approach the two positively charged particles have slowed to a stop:

Etotal = 2(0.5)mv2 + kQq/r

2.67 X 10-14 J = 0 + (9 x 109)(1.6 X 10-19 C)(1.6 X 10-19 C)/r

r = 8.63 X 10-15 m

2. The potential energy of the system is the sum of the potential energies of each pair of charges:
U = U1,2 + U1,3 + U2,3

U1,2 = (9 x 109)(4 x 10-6 C)(-2 x 10-6 C)/(0.30 m) = -0.240 J

U1,3 = (9 x 109)(4 x 10-6 C)(5 x 10-6 C)/(0.424 m) = 0.425 J

U2,3 = (9 x 109)(-2 x 10-6 C)(5 x 10-6 C)/(0.30 m) = -0.300 J

U = -0.115 J

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