Physics A Level
Chapter 21: Uniform electric fields 21.4 Force on a charge
Physics A Level
Chapter 21: Uniform electric fields 21.4 Force on a charge
Now we can calculate the force F on a charge Q in the uniform field between two parallel plates. We have to combine the general equation for field strength $E = \frac{F}{Q}$ with the equation for the strength of a uniform field $E = - \frac{V}{d}$.
This gives:
$F = QE = - \frac{{QV}}{d}$
For an electron with charge −e, this becomes:
$F = \frac{{eV}}{d}$
Figure 21.14 shows a situation where this force is important. A beam of electrons is entering the space between two charged parallel plates. How will the beam move?
We have to think about the force on a single electron. In the diagram, the upper plate is negative relative to the lower plate, and so the electron is pushed downwards. (You can think of this simply as the negatively charged electron being attracted by the positive plate, and repelled by the negative plate.)
If the electron were stationary, it would accelerate directly downwards. However, in this example, the electron is moving to the right. Its horizontal velocity will be unaffected by the force, but as it moves sideways it will also accelerate downwards. It will follow a curved path, as shown. This curve is a parabola.
Note that the force on the electron is the same at all points between the plates, and it is always in the same direction (downwards, in this example).
This situation is equivalent to a ball being thrown horizontally in the Earth’s uniform gravitational field (Figure 21.15). It continues to move at a steady speed horizontally, but at the same time it accelerates downwards. The result is the familiar curved trajectory shown. For the electron described, the force of gravity is tiny–negligible compared to the electric force on it.
Questions
9) In Figure 21.16, two parallel plates are shown, separated by $25 cm$.
a: Copy the diagram and draw field lines to represent the field between the plates.
b: What is the potential difference between points A and B?
c: What is the electric field strength at C, and at D?
d: Calculate the electric force on a charge of $ + 5\,\mu C$ placed at C. In which direction does the force act?
10) A particle of charge $ + 2\,\mu C$ is placed between two parallel plates, $10 cm$ apart and with a potential difference of $5 kV$ between them. Calculate the field strength between the plates, and the force
exerted on the charge.
11) We are used to experiencing accelerations that are usually less than $10\,m\,{s^{ - 2}}$. For example, when we fall, our acceleration is about $9.8\,m\,{s^{ - 2}}$. When a car turns a corner sharply at speed, its acceleration is unlikely to be more than $5\,m\,{s^{ - 2}}$. However, if you were an electron, you would be used to experiencing much greater accelerations than this. Calculate the acceleration of an electron in a television tube where the electric field strength is $50000\,V\,c{m^{ - 1}}$. (Electron charge $ - e = - 1.6 \times {10^{ - 19}}C$; electron mass ${m_e} = 9.11 \times {10^{ - 31}}\,kg$.)
12) a: Use a diagram to explain how the electric force on a charged particle could be used to separate a beam of electrons (${e^ - }$) and positrons (${e^ + }$) into two separate beams. (A positron is a positively charged particle that has the same mass as an electron but opposite charge. Positron–electron pairs are often produced in collisions in a particle accelerator.)
b: Explain how this effect could be used to separate ions that have different masses and charges.
EXAM-STYLE QUESTIONS
1) A pair of charged parallel plates are arranged horizontally in a vacuum.
The upper plate carries a negative charge and the lower plate is earthed.
An electron enters the space between the plates at right angles to the electric field.
In which direction is the electric field between the plates and in which direction is the force on the electron? [1]
| Force on the electron | Electric field strength | |
| downwards towards the lower plate | downwards towards the lower plate | A |
| upwards towards the upper plate | downwards towards the lower plate | B |
| downwards towards the lower plate | upwards towards the upper plate | C |
| upwards towards the upper plate | upwards towards the upper plate | D |
2) A pair of charged parallel plates are 2.0 cm apart and there is a potential difference of $5.0 kV$ across the plates.
A charged ion between the plates experiences a force of $1.2 \times {10^{ - 13}}N$ due to the field.
What is the charge on the ion? [1]
A: $1.6 \times {10^{ - 19}}C$
B: $4.8 \times {10^{ - 19}}C$
C: $2.51.6 \times {10^{ - 15}}C$
D: $4.0 \times {10^{ - 6}}C$
3) Figure 21.4 shows apparatus used to investigate the field between a pair of charged, parallel plates.
a: Explain why the piece of gold foil deflects in the manner shown. [1]
b: and explain what would be observed if the gold foil momentarily touched the negatively charged plate. [2]
[Total: 3]
4) A charged dust particle in an electric field experiences a force of $4.4 \times {10^{ - 13}}N$. The charge on the particle is $8.8 \times {10^{ - 17}}C$. Calculate the electric field strength. [2]
5) Calculate the potential difference that must be applied across a pair of parallel plates, placed 4 cm apart, to produce an electric field of $4000\,V\,{m^{ - 1}}$. [2]
6) A potential difference of $2.4 kV$ is applied across a pair of parallel plates. The electric field strength between the plates is $3.0 \times {10^4}\,V\,{m^{ - 1}}$.
a: Calculate the separation of the plates. [2]
The plates are now moved so that they are $2.0 cm$ apart. Calculate the b: electric field strength produced in this new position. [2]
[Total: 4]
7) A variable power supply is connected across a pair of parallel plates. The potential difference across the plates is doubled and the distance between the plates is decreased to one-third of the original. State by what factor the electric field changes. Explain your reasoning. [3]
8) This diagram shows a positively charged sphere hanging by an insulating thread close to an earthed metal plate.
a: Copy the diagram and draw five lines to show the electric field near the plate and the sphere. [3]
b: Explain why the sphere is attracted towards the metal plate. [2]
c: The sphere is now replaced with a similar negatively charged sphere.
i- Explain what would be observed when the sphere is brought near to the earthed metal plate. [2]
ii- Describe any changes to the electric field that would occur. [1]
[Total: 8]
9) This diagram shows a proton as it moves between two charged parallel plates.
The charge on the proton is $ + 1.6 \times {10^{ - 19}}C$.
a: Copy the diagram and draw the electric field between the parallel plates. [2]
The force on the proton when it is at position B is $6.4 \times {10^{ - 14}}N$.
b: In which direction does the force on the proton act when it is at position B? [1]
c: What will be the magnitude of the force on the proton when it is at position C? [1]
d: Calculate the electric field strength between the plates. [2]
e: Calculate the potential difference between the plates. [2]
[Total: 8]
10) a: Define what is meant by the electric field strength at a point. [2]
In a particle accelerator, a proton, initially at rest, is accelerated between two metal plates, as shown.
b: Calculate the force on the proton due to the electric field. [3]
c: Calculate the work done on the proton by the electric field when it moves from plate A to plate B. [2]
d: State the energy gained by the proton. [1]
e: Assuming that all this energy is converted to kinetic energy of the proton, calculate the speed of the proton when it reaches plate B. [3]
(Charge on a proton $ = + 1.6 \times {10^{ - 19}}C$; mass of a proton $ = 1.7 \times {10^{ - 27}}\,kg$.)
[Total: 11]
11) a: This diagram shows the structure of a spark plug in an internal combustion engine. The magnified section shows the end of the spark plug, with some of the lines of force representing the electric field.
i- Copy the field lines from the diagram. On your copy, draw arrows on the lines of force to show the direction of the field. [1]
ii- What evidence does the diagram give that the field is strongest near the tip of the inner electrode? [1]
b: The gap between the inner and outer electrodes is $1.25 mm$ and a field strength of $5.0 \times {10^6}\,N\,{C^{ - 1}}$ is required for electrical breakdown. Estimate the minimum potential difference that must be applied across the inner and outer electrodes for a spark to be produced. (You may treat the two electrodes as a pair of parallel plates.) [2]
c: When an electron is accelerated through a potential drop of approximately $20 V$ it will have sufficient energy to ionise a nitrogen atom. Show that an electron must move $4.0\,\mu m$ to gain this energy. [2]
[Total: 6]
SELF-EVALUATION CHECKLIST
After studying the chapter, complete a table like this:
| I can | See topic… | Needs more work | Almost there | Ready to move on |
| understand that an electric field is a field of force | 21.2 | |||
| define electric field as force per unit positive charge | 21.3 | |||
| represent an electric field by means of field lines | 21.3 | |||
| understand that the field between parallel plates is uniform | 21.3 | |||
|
recall and use the formula: $E = - \frac{{\Delta V}}{{\Delta x}}$ |
21.3 | |||
| describe the paths taken by charged particles as they pass through a uniform electric field. | 21.4 |