Physics A Level
Chapter 22: Coulomb’s law 22.5 Gravitational and electric fields
Physics A Level
Chapter 22: Coulomb’s law 22.5 Gravitational and electric fields
There are obvious similarities between the ideas we have used in this chapter to describe electric fields and those we used in Chapter 17 for gravitational fields. This can be helpful, or it can be confusing! The summary given in Table 22.1 is intended to help you to sort them out.
An important difference is this: electric charges can be positive or negative, so they can attract or repel.
There are no negative masses, so there is only attraction in a gravitational field.
| Electric fields | Gravitational fields |
|
Origin arise from electric charges |
Origin arise from masses |
|
Vector forces both electrical attraction and repulsion are possible |
Vector forces only gravitational attraction, no repulsion |
|
All electric fields field strength $E = \frac{F}{Q}$ |
All gravitational fields field strength $g = \frac{F}{m}$ |
|
Units F in N, E in $N\,{C^{ - 1}}$ or $V\,{m^{ - 1}}$ |
Units F in N, g in $N\,k{g^{ - 1}}$ or $m\,{s^{ - 2}}$ |
|
Uniform electric fields parallel electric field lines |
Uniform gravitational fields parallel gravitational field lines |
|
Spherical electric fields radial field lines
|
Spherical gravitational fields radial field lines
|
|
Electric potential given by: $V = \frac{Q}{{4\pi {\varepsilon _0}r}}$
|
Gravitational potential Electric potential given by: $\phi = \frac{{GM}}{r}$
|
finity
Question
You will need the following data to answer the question.
$proton\,mass = 1.67 \times {10^{ - 27}}\,kg$
$proton\,charge = + 1.60 \times {10^{ - 19}}\,C$
${\varepsilon _0} = 8.85 \times {10^{ - 12}}\,F\,{m^{ - 1}}$
$G = 6.67 \times {10^{ - 11}}\,N\,{m^2}\,k{g^{ - 2}}$
6) Two protons in the nucleus of an atom are separated by a distance of ${10^{ - 15}}\,m$. Calculate the electrostatic force of repulsion between them, and the force of gravitational attraction between them.
(Assume the protons behave as point charges and point masses.) Is the attractive gravitational force enough to balance the repulsive electrical force? What does this suggest to you about the forces between protons within a nucleus?
EXAM-STYLE QUESTIONS
1) How does the potential V change with the distance r from a point charge? [1]
A: $V \propto r$
B: $V \propto {r^2}$
C: $V \propto {r^{ - 1}}$
D: $V \propto {r^{ - 2}}$
2) The electric field strength $20 cm$ from an isolated point charge is $1.9 \times {10^4}\,N\,{C^{ - 1}}$.
What is the electric field strength $30 cm$ from the charge? [1]
A: $8.4 \times {10^3}\,N\,{C^{ - 1}}$
B: $1.3 \times {10^4}\,N\,{C^{ - 1}}$
C: $2.9 \times {10^4}\,N\,{C^{ - 1}}$
D: $4.3 \times {10^4}\,N\,{C^{ - 1}}$
3) On a copy of this diagram, draw the electric fields between the charged objects. [5]
4) Two parallel plates are $4 cm$ apart and have a potential difference of $2.5 kV$ between them.
a: Calculate the electric field strength between the plates. [2]
b: A small piece of dust carrying a charge of $+2.4 nC$ moves into the space between the plates.
i- Calculate the force on the dust particle. [2]
ii- The mass of the dust particle is $4.2 mg$. Calculate the acceleration of the particle towards the negative plate. [2]
[Total: 6]
5) A small sphere carries a charge of $2.4 \times {10^{ - 9}}\,C$. Calculate the electric field strength at a distance of:
a: $2 cm$ from the centre of the sphere [2]
b: $4 cm$ from the centre of the sphere. [2]
[Total: 4]
6) A conducting sphere of diameter $6.0 cm$ is mounted on an insulating base. The sphere is connected to a power supply that has an output voltage of $20 kV$.
a: Calculate the charge on the sphere. [3]
b: Calculate the electric field strength at the surface of the sphere. [2]
[Total: 5]
7) The nucleus of a hydrogen atom carries a charge of $ + 1.60 \times {10^{ - 19}}\,C$.
Its electron is at a distance of $1.05 \times {10^{ - 10}}\,m$ from the nucleus.
Calculate the ionisation potential of hydrogen. [3]
(Hint: This is equal to the work per unit charge needed to remove the electron to infinity.)
8) a: Define electric field strength. [2]
b: Two charged conducting spheres, each of radius $1.0 cm$, are placed with their centres $10 cm$ apart, as shown.
Sphere A carries a charge of $ + 2.0 \times {10^{ - 9}}\,C$.
The graph shows how the electric field strength between the two spheres varies with distance x.
i- Determine the field strength 5.0 cm from the centre of sphere A [2]
ii- Use your result to i to calculate the charge on sphere B. [3]
c: i- Sphere B is now removed. Calculate the potential at the surface of sphere A. [2]
ii- Suggest and explain how the potential at the surface of sphere A would compare before and after sphere B was removed. [2]
[Total: 11]
9) An $\alpha - $particle emitted in the radioactive decay of radium has a kinetic energy of $8.0 \times {10^{ - 13}}\,J$.
a: i- Calculate the potential difference that an $\alpha - $particle, initially at rest, would have to be accelerated through to gain this energy. [2]
ii- Calculate the speed of the α-particle at this kinetic energy. [3]
b: This diagram shows the path of an $\alpha - $particle of this energy as it approaches a gold nucleus head-on.
i- State the speed of the α-particle at its point of closest approach to the gold nucleus. [1]
ii- Write down the kinetic energy of the $\alpha - $particle at this point. [1]
iii- Write down the potential energy of the $\alpha - $particle at this point. [1]
c: Use your answer to part b iii to show that the $\alpha - $particle will reach a distance of $4.5 \times {10^{ - 14}}\,m$ from the centre of the gold nucleus. [2]
d: Suggest and explain what this information tells us about the gold nucleus. [2]
($Mass\,of\,an\,\alpha - particle = 6.65 \times {10^{ - 27}}\,kg$; $charge\,on\,an\,\alpha - particle = + 2e$;
$charge\,on\,a\,gold\,nucleus = + 79e$
10) a: Define electric potential at a point. [2]
b: This graph shows the electrical potential near an antiproton.
i- Determine the potential at a distance $0.53 \times {10^{ - 10}}\,m$ from the antiproton. [2]
ii- Determine the potential energy a positron would have at this distance. [2]
c: Use the graph to determine the electric field at this distance from the antiproton. [2]
[Total: 8]
11) This diagram shows a conducting sphere of radius $0.80 cm$ carrying a charge of $ + 6.0 \times {10^{ - 8}}\,C$ resting on a balance.
a: Calculate the electric field at the surface of the sphere. [2]
b: An identical sphere carrying a charge of $ - 4.5 \times {10^{ - 5}}\,C$ is held so that its centre is $5.0 cm$ vertically above the centre of the first sphere.
i- Calculate the electric force between the two spheres. [2]
ii- Calculate the new reading on the balance. [1]
c: The second sphere is moved vertically downwards through $1.5 cm$.
Calculate the work done against the electric field in moving the sphere. [3]
[Total: 8]
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 the nature of the electric field | 22.1 | |||
| represent and interpret an electric field using field lines | 22.4 | |||
| recall and use Coulomb’s law: | 22.2 | |||
| understand that electric field g is defined as the electric force per unit coulomb | 22.5 | |||
| derive from Coulomb’s law of gravitation: | 22.3 | |||
| recall and use the equation: | 22.3 | |||
| recall and use: | 22.4 | |||
| define electric potential at a point, V, as the work done in bringing unit charge from infinity to that point | 22.4 | |||
| recognise that the electric potential at infinity is zero | 22.4 | |||
| recognise that the electric potential increases as you move closer to a positively charged object | 22.4 | |||
| recognise that the electric potential decreases as you move closer to a negatively charged object | 22.4 | |||
| recall and use the formula: gravitational potential |
22.4 | |||
| use the formula: | 22.4 | |||
| understand that the electric potential energy of two point masses is equal to: | 22.4 |