16.3 Capacitors  (Page 3/3)

If the voltage is removed, the capacitor will discharge. The electrons begin to move because in the absence of the voltagesource, there is now a net electric field. This field is due to the imbalance of charge on the electrodes–the field across thedielectric. Just as the electrons flowed to the positive electrode when the capacitor was being charged, during discharge, theelectrons flow to negative electrode. The charges cancel, and there is no longer an electric field across the dielectric.

Real-world applications: capacitors

Capacitors are used in many different types of circuitry. In car speakers, capacitors are often used to aid the power supply whenthe speakers require more power than the car battery can provide. Capacitors are also used in processing electronic signals incircuits, such as smoothing voltage spikes due to inconsistent voltage sources. This is important for protecting sensitive electronic components in a circuit.

Summary

1. Objects can be positively , negatively charged or neutral .
2. Charged objects feel a force with a magnitude. This is known as Coulomb's law:
   $$F=k\frac{Q_1{Q}_2}{r^2}$$
3. The electric field due to a point charge is given by the equation:
   $$E=\frac{kQ}{r^2}$$
4. The force is attractive for unlike charges and repulsive for like charges.
5. Electric fields start on positive charges and end on negative charges.
6. A charge in an electric field, just like a mass under gravity, has potential energy which is related to the work to move it.
7. A capacitor is a device that stores charge in a circuit.
8. The electrical potential energy between two point charges is given by:
   $$U=\frac{k{Q}_1{Q}_2}{r^2}$$
9. Potential difference is measured in volts and is given by the equation:
   $$V=\frac{W}{q}$$
10. The electric field is constant between equally charged parallel plates. The electric field is given by:
    $$E=\frac{V}{d}$$
11. The capacitance of a capacitor can be calculated as
    $$C=\frac{Q}{V}=\frac{{ϵ}_{0}A}{d}$$

Exercises - electrostatics

1. Two charges of $+3\mathrm{nC}$ and $-5\mathrm{nC}$ are separated by a distance of $40\mathrm{cm}$ . What is the electrostatic force between the two charges?
2. Two insulated metal spheres carrying charges of $+6\mathrm{nC}$ and $-10\mathrm{nC}$ are separated by a distance of 20 mm.
   1. What is the electrostatic force between the spheres?
   2. The two spheres are touched and then separated by a distance of $60\mathrm{mm}$ . What are the new charges on the spheres?
   3. What is new electrostatic force between the spheres at this distance?
3. The electrostatic force between two charged spheres of $+3\mathrm{nC}$ and $+4\mathrm{nC}$ respectively is $0,04\mathrm{N}$ . What is the distance between the spheres?
4. Calculate the potential difference between two parallel plates if it takes $5000\mathrm{J}$ of energy to move $25\mathrm{C}$ of charge between the plates?
5. Draw the electric field pattern lines between:
   1. two equal positive point charges.
   2. two equal negative point charges.
6. Calculate the electric field between the plates of a capacitor if the plates are $20\mathrm{mm}$ apart and the potential difference between the plates is $300\mathrm{V}$ .
7. Calculate the electrical potential energy of a $6\mathrm{nC}$ charge that is $20\mathrm{cm}$ from a $10\mathrm{nC}$ charge.
8. What is the capacitance of a capacitor if it has a charge of $0,02\mathrm{C}$ on each of its plates when the potential difference between the plates is $12\mathrm{V}$ ?
9. [SC 2003/11] Two small identical metal spheres, on insulated stands, carry charges - $q$ and $+3q$ respectively. When the centres of the spheres are separated by a distance $d$ the one exerts an electrostatic force of magnitude $F$ on the other.

   

   The spheres are now made to touch each other and are then brought back to the same distance $d$ apart. What will be the magnitude of the electrostatic force which one sphere now exerts on the other?
   1. $\frac{1}{4}F$
   2. $\frac{1}{3}F$
   3. $\frac{1}{2}F$
   4. $3F$
10. [SC 2003/11] Three point charges of magnitude +1 $\mu$ C, +1 $\mu$ C and -1 $\mu$ C respectively are placed on the three corners of an equilateral triangle as shown.

    

    Which vector best represents the direction of the resultant force acting on the -1 $\mu$ C charge as a result of the forces exerted by the other two charges?

    (a)	(b)	(c)	(d)

11. [IEB 2003/11 HG1 - Force Fields]
    1. Write a statement of Coulomb's law.
    2. Calculate the magnitude of the force exerted by a point charge of +2 nC on another point charge of -3 nC separated by a distance of 60 mm.
    3. Sketch the electric field between two point charges of +2 nC and -3 nC, respectively, placed 60 mm apart from each other.
12. [IEB 2003/11 HG1 - Electrostatic Ping-Pong] Two charged parallel metal plates, X and Y, separated by adistance of 60 mm, are connected to a DC supply of emf 2 000 V in series with a microammeter. An initially uncharged conductingsphere (a graphite-coated ping pong ball) is suspended from an insulating thread between the metal plates as shown in thediagram.

    

    When the ping pong ball is moved to the right to touch the positive plate, it acquires a charge of +9 nC. It is thenreleased. The ball swings to and fro between the two plates, touching each plate in turn.
    1. How many electrons have been removed from the ball when it acquires a charge of +9 nC?
    2. Explain why a current is established in the circuit.
    3. Determine the current if the ball takes 0,25 s to swing from Y to X.
    4. Using the same graphite-coated ping pong ball, and the same two metal plates, give TWO ways in which this current could be increased.
    5. Sketch the electric field between the plates X and Y.
    6. How does the electric force exerted on the ball change as it moves from Y to X?
13. [IEB 2005/11 HG] A positive charge $Q$ is released from rest at the centre of a uniform electric field.

    

    How does $Q$ move immediately after it is released?
    1. It accelerates uniformly.
    2. It moves with an increasing acceleration.
    3. It moves with constant speed.
    4. It remains at rest in its initial position.
14. [SC 2002/03 HG1] The sketch below shows two sets of parallel plates which areconnected together. A potential difference of 200 V is applied across both sets of plates. The distances between the two sets ofplates are 20 mm and 40 mm respectively.

    

    When a charged particle Q is placed at point R, it experiences a force of magnitude $F$ . Q is now moved to point P, halfway between plates AB and CD. Q now experiences a force of magnitude .
    1. $\frac{1}{2}F$
    2. $F$
    3. $2F$
    4. $4F$
15. [SC 2002/03 HG1] The electric field strength at a distance $x$ from a point charge is $E$ . What is the magnitude of the electric field strength at a distance $2x$ away from the point charge?
    1. $\frac{1}{4}E$
    2. $\frac{1}{2}E$
    3. $2E$
    4. $4E$
16. [IEB 2005/11 HG1] An electron (mass 9,11 $\times$ 10 ${}^{-31}$ kg) travels horizontally in a vacuum. It enters the shaded regions between twohorizontal metal plates as shown in the diagram below.

    

    A potential difference of 400 V is applied across the places which are separated by 8 mm. The electric field intensity in the shaded region between themetal plates is uniform. Outside this region, it is zero.
    1. Explain what is meant by the phrase “the electric field intensity is uniform” .
    2. Copy the diagram and draw the following:
       1. The electric field between the metal plates.
       2. An arrow showing the direction of the electrostatic force on the electron when it is at P .
    3. Determine the magnitude of the electric field intensity between the metal plates.
    4. Calculate the magnitude of the electrical force on the electron during its passage through the electric field between the plates.
    5. Calculate the magnitude of the acceleration of the electron (due to the electrical force on it) during its passage through the electric field between the plates.
    6. After the electron has passed through the electric field between these plates, it collides with phosphorescent paint on a TV screen and this causes the paint to glow. What energy transfer takes place during this collision?
17. [IEB 2004/11 HG1] A positively-charged particle is placed in a uniform electric field. Which of the following pairs of statements correctly describes the potential energy of the charge, and the force which the charge experiences in this field?Potential energy — Force
    1. Greatest near the negative plate — Same everywhere in the field
    2. Greatest near the negative plate — Greatest near the positive and negative plates
    3. Greatest near the positive plate — Greatest near the positive and negative plates
    4. Greatest near the positive plate — Same everywhere in the field
18. [IEB 2004/11 HG1 - TV Tube] A speck of dust is attracted to a TV screen. The screen isnegatively charged, because this is where the electron beam strikes it. The speck of dust is neutral.
    1. What is the name of the electrostatic process which causes dust to be attracted to a TV screen?
    2. Explain why a neutral speck of dust is attracted to the negatively-charged TV screen?
    3. Inside the TV tube, electrons are accelerated through a uniform electric field. Determine the magnitude of the electric force exerted on an electron when it accelerates through a potential difference of 2 000 V over a distance of 50 mm.
    4. How much kinetic energy (in J) does one electron gain while it accelerates over this distance?
    5. The TV tube has a power rating of 300 W. Estimate the maximum number of electrons striking the screen per second.
19. [IEB 2003/11 HG1] A point charge is held stationary between two charged parallel plates that are separated by a distance d. The point charge experiences an electrical force F due to the electric field E between the parallel plates.What is the electrical force on the point charge when the plate separation is increased to 2d?
    1. $\frac{1}{4}$ F
    2. $\frac{1}{2}$ F
    3. 2 F
    4. 4 F
20. [IEB 2001/11 HG1] - Parallel Plates A distance of 32 mm separates the horizontal parallel plates A and B. B is at a potential of +1 000 V.

    

    1. Draw a sketch to show the electric field lines between the plates A and B.
    2. Calculate the magnitude of the electric field intensity (strength) between the plates. A tiny charged particle is stationary at S, 8 mm below plate A that is at zero electrical potential. It has a charge of 3,2 $\times$ 10 ${}^{-12}$ C.
    3. State whether the charge on this particle is positive or negative.
    4. Calculate the force due to the electric field on the charge.
    5. Determine the mass of the charged particle. The charge is now moved from S to Q.
    6. What is the magnitude of the force exerted by the electric field on the charge at Q?
    7. Calculate the work done when the particle is moved from S to Q.