AQA A Level Physics

Topic Questions

7.5 Electric Potential

1a3 marks

Define electric potential.

1b2 marks
(i)
State whether electric potential is a scalar or vector quantity.
(ii)
Give a reason for your answer.
1c2 marks

State what happens to the magnitude of the electric potential the further a positive test charge is moved from: 

(i)         A positive charge 

(ii)        A negative charge

1d2 marks

A positive test charge, +q, is moved away from the surface of an object with charge +Q, as shown in Figure 1

Figure 1

7-5-s-q--q1a-fig1-easy-aqa-a-level-physics

On Figure 2 below, sketch a graph to show how the electric potential varies as the test charge is moved from the surface of the positive charge.  

Figure 27-5-s-q--q1a-fig2-easy-aqa-a-level-physics

 

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2a4 marks

The equation to calculate the electric potential in the field due to a point charge is given below: 

         Vfraction numerator 1 over denominator 4 πε subscript 0 end fraction Q over r   

Define each of the symbols used in the equation.

2b3 marks

A sphere of radius 12 cm is charged to a potential of + 220 kV. 

Calculate the charge stored on the surface of the sphere.

2c2 marks

Assume the charge stored on the sphere calculated in part (b) acts as a point charge. 

Calculate the electric potential at a point 30 cm from this point charge.

2d4 marks

A proton is moved from infinity to a point in the field produce by the charge in part (c). 

Using your answer to part (c), calculate:

(i)
the potential difference between infinity and the point 30 cm away from the charge described in part (c)
(ii)
the work done on the proton to move it from infinity to a point 30 cm away from the charge described in part (c).

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3a3 marks

A lithium nucleus contains 3 protons. 

Calculate the total charge of a lithium nucleus

3b2 marks

The lithium nucleus can be assumed to be a point charge. 

Calculate the electric potential at a distance of 1.3 × 10–14 m from the lithium nucleus.

3c1 mark

Figure 1 shows the how the electric potential varies as the distance from the lithium nucleus increases. 

Figure 1

7-5-s-q--q3c-easy-aqa-a-level-physics

State which feature of the graph would allow the electric field strength at a particular point due to the lithium nucleus to be calculated.

3d2 marks

On Figure 2 below, sketch a graph to show how the magnitude of the electric field strength varies as the distance from the lithium nucleus is increased.  

Figure 2

7-5-s-q--q3d-easy-aqa-a-level-physics

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4a1 mark

An isolated point charge, of magnitude Q, is situated inside a vacuum.  The electric potential has a value of +1.2 J C–1 at a distance of 1.8 × 10–10 m from the point charge. 

State the significance of a positive sign for the electric potential.

4b3 marks

Calculate the magnitude of the charge Q.

4c2 marks

An electron is moved from a point in the electric field surrounding Q where the electric potential is + 1.2 J C–1 to a point where the electric potential is + 0.50 J C–1

Calculate the electrical potential difference between these two points.

4d3 marks
(i)

Calculate the work done moving the electron from an electric potential of +1.2 J C–1 to an electric potential of +0.50 J C–1.

(ii)
State whether the work calculated in (i) is done by the electric field produced by charge Q or against the electric field produced by charge Q.

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5a1 mark

State what is meant by an electrostatic equipotential surface.

5b2 marks

Figure 1 shows two oppositely charged metal plates, set up such that a uniform electric field exists between them. 

Figure 1

7-5-s-q--q5b-easy-aqa-a-level-physics

Draw 4 electrical equipotential lines between the two plates shown in Figure 1.

5c3 marks

Figure 2 below shows the field lines and equipotential lines around an isolated positive point charge.  A, B, C and D are 4 points within the electric field produced by the positive point charge.

Figure 2

7-5-s-q--q5c-easy-aqa-a-level-physics

State whether the electric potential increases, decreases or remains the same between:

(i)
A and B
(ii)
A and C
(iii)
D and B
5d6 marks

Figure 3 shows the equipotential lines above a positive plate.  The magnitude of the electric potential is written beside each equipotential line.  A, B and C are 3 points within the electric field produced by the positive plate. 

Figure 3

7-5-s-q--q5d-easy-aqa-a-level-physics

An electron is moved from A to B and then from B to C.  

Calculate: 

(i)
The electric potential difference between A and B. 
(ii)
The work done moving an electron between A and B
(iii)
The total work done moving an electron from A to B and then from B to C.         

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1a3 marks

Calculate the kinetic energy of an alpha  particle travelling at a speed of 3.50 × 107 m s–1 when relativistic effects are ignored.

1b4 marks

Calculate the closest distance of approach for a head-on collision between an  alpha particle travelling at a speed of 3.50 × 107 m s–1 and a gold nucleus for which the proton number is 79.

Assume that the gold nucleus remains stationary during the collision.

1c2 marks

The alpha particle is fired towards a polonium nucleus, which contains more protons than the gold nucleus. The alpha particle is given the same initial kinetic energy as in part (a).

State and explain, without further calculation, any changes that occur to the closest distance of approach. You can ignore any recoil effects.

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2a4 marks

The simplest model of a Hydrogen atom shows an electron moving around a positive nucleus in a circular orbit. The proton and the electron are small enough to be considered point charges and the distance between them is 5.3 × 10-11 m. 

Calculate the average electric current along the electron’s orbit.

2b4 marks

Show that the total energy of an electron orbiting a proton can be written as:

         E = - fraction numerator 1 over denominator 8 πε subscript 0 end fraction e squared over r

Where:

         Mass of the electron, m subscript e

         Radius of the orbit, r

         Magnitude of charge on an electron, e

         Permittivity of free space, ε0

2c2 marks

When the electron orbits around the nucleus it can be considered an oscillating charge, and hence it emits electromagnetic radiation of the same frequency. 

Use the equation found in part (b) to determine what would happen to the radius of the electrons orbit due to the emission of electromagnetic radiation.

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3a3 marks

Three charges are fixed at the corners of a right-angled triangle as shown in Figure 1.The length of the horizontal and vertical side is d. 

Figure 1

7-5-s-q--q3a-hard-aqa-a-level-physics

Show that the electric potential at point P, halfway between the -2Q and -6Q charge is:

            negative fraction numerator 2 Q over denominator square root of 2 d πε subscript 0 end fraction

3b5 marks

Before the discovery of quarks, scientists speculated that the subatomic particles might be made up of smaller particles. 

If an electron was made up of three smaller, identical particles with charge q which are brought in from an infinite distance to the vertices of an equilateral triangle, it would have the arrangement shown in Figure 2.

Figure 2

7-5-s-q--q3b-hard-aqa-a-level-physics

Show that the work done in forming an electron consisting of 3 identical particles, as shown in Figure 2, is:

                  fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator e squared over denominator 3 r end fraction

Where:

  • The distance r is the radius of an electron which is 2.82 fm
  • e is the charge of an electron
  • epsilon subscript 0 is the permittivity of free space
3c2 marks

Figure 3 shows the structure of an electron gun. Electrons are released from a cathode and accelerated towards an anode. 

Figure 3

7-5-s-q--q3c-hard-aqa-a-level-physics

The electrons leave the electron gun at 10% of the speed of light. Calculate the potential difference between the cathode and the anode. 

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4a3 marks

Calculate the electrostatic potential energy, in keV, of two hydrogen nuclei at a distance of 2.0 fm apart.

4b2 marks

Two protons in an accelerator are moving in opposite directions at the same initial speed and collide head-on with each other. The least distance apart of the two protons is 2.0 fm.

By considering the conservation of energy, estimate the initial kinetic energy, in MeV, of each proton.

4c3 marks

The fusion of a helium-3 nucleus and a helium-4 nucleus will occur if they are separated by no more than 3.5 fm.

Calculate the minimum total kinetic energy of the nuclei required for fusion to occur between the helium-3 and helium-4 nuclei.

4d3 marks

Deduce whether nuclear fusion would occur between a helium-3 nucleus and a helium-4 nucleus if they were heated to a temperature of 4 × 109 K in a gaseous plasma.

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5a1 mark

A science fiction film director is planning for a battle scene between two spacecrafts. The first spacecraft uses an electron gun to fire a beam of electrons at the second spacecraft from close range. The electron beam is created by accelerating electrons from rest between electrodes with a potential difference of 120 V. 

To shield against the attack, the second aircraft creates a uniform electric field around itself.

Calculate the strength of the electric shield if the electrons fired from the electron beam are stopped after 85 m.

5b3 marks

After the failure of the first spacecraft to break through the electric shield of the second spacecraft a new weapon is to be designed. Instead of firing electrons, research is carried out to see if firing negatively charged ions with a charge of –2e and a mass of 2.26 × 10-26 kg would be more effective.

Calculate the magnitude of the minimum velocity at which these ions would need to be fired if they are to strike the second spacecraft from a distance of 1 km.

Assume that the second spacecraft uses the same electric field as in part (a) to shield itself and that the electric field is uniform.

5c3 marks

Another option to attack the second spacecraft is to create a superweapon which can be fired from their home planet. As this weapon will fired from such a long way away from the second spacecraft, the spaceship and shield can be modelled as a charged particle carrying a charge of -130 C. The electrons fired by the superweapon have a kinetic energy of 12 MeV.

Calculate how close the electrons will come to the second spacecraft before they are stopped by the shield.

5d4 marks

The final solution to destroy the second spacecraft is to design a weapon which fires alpha particles of charge +2e and mass 6.50 × 10-27 kg from the first spacecraft.

If these particles were fired with a velocity of 50 km s-1 from a distance of 100 m calculate the speed at which they would hit the second spacecraft.

Assume that the second spacecraft produces the same electric field as in part (a) as its shield.

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1a2 marks

An ion of charge +3e experiences an electrostatic force of 7.3 × 10–15 N in an uniform electric field, as shown in Figure 1. 

Figure 1

7-5-s-q--q1a-medium-aqa-a-level-physics

Calculate the kinetic energy gained by the ion when it is accelerated by the field through a distance of 51 mm parallel to the field lines.

1b3 marks

Calculate the potential difference of the length of electric field travelled by the ion.

1c2 marks

The mass of the ion is 8.35 × 10–27 kg. 

Calculate the speed of the ion at the end of the acceleration.

1d3 marks

The electric field is now in a direction perpendicular to the ion as shown in Figure 2. 

Figure 2

7-5-s-q--q1d-medium-aqa-a-level-physics

The ion is moved from X to Y and then from Y to Z. 

If the distance XY is 4m and YZ is 5m, calculate the change in potential energy of the charge when it is moved from X to Z.

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2a3 marks

Two small charged spheres P and Q may be assumed to be point charges located at their centres. The particles are in a vacuum. 

Particle Q is in a fixed position. Particle P is moved along the line joining the two charges, as shown in Figure 1. 

Figure 1

7-5-s-q--q2a-fig-1-medium-aqa-a-level-physics

The variation with separation x of the electric potential energy E subscript P of particle P is shown in Figure 2.

Figure 2

7-5-s-q--q2a-fig-2-medium-aqa-a-level-physics

State and explain what feature of the graph in Figure 2 is equal to the electric force on particle P.

2b2 marks

The magnitude of the charge for both P and Q is 2e. 

Calculate the separation of the particles at the point where particle P has an electric potential energy equal to –12.7 eV.

2c4 marks

Using the graph in Figure 2, estimate the electric field strength at a separation of 0.6 nm between P and Q.

2d4 marks

By reference to the graph in Figure 2, state and explain:

(i)
Whether the two charges have the same, or opposite charge.
(ii)
The effect, if any, on the shape of the graph when the charge on particle Qis doubled.

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3a3 marks

Figure 1

7-5-s-q--q3a-medium-aqa-a-level-physics

Figure 1 shows two charges, +6 µC and –20 µC, 150 mm apart. 

Calculate the distance, in mm, from the +6 µC charge to the point between the two charges, where the resultant electric potential is zero.

3b4 marks

On Figure 2, draw a graph of the electric potential against distance from the +6 µC charge to the –20 µC charge. Label any relevant points. 

Figure 2

7-5-s-q--q3b-medium-aqa-a-level-physics

3c3 marks

Point Plies 60 mm below +6 µC charge, as shown in Figure 3. 

Figure 3

7-5-s-q--q3c-medium-aqa-a-level-physics

Calculate the electric potential at point P due to the ­–20 µC charge.

3d3 marks

Calculate the total electric potential at point P.

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4a3 marks

The Earth can be considered to have a concentrated charge at its centre which is distributed uniformly over the Earth’s surface.  The electric field strength 1 000 km from the surface of the Earth is 62.8 N C-1.  

   Calculate the charge per square metre on the surface of the Earth.           

            The radius of the Earth is 6.37 × 106 m

4b3 marks

During an electrical storm water droplets in the clouds become negatively charged.  The negative charges in the bottom of the cloud have such a high concentration that they force the electrons on the Earth's surface deep into the ground.  This results in the ground having a positive charge and the cloud having a negative charge. 

A raindrop in one of the storm clouds is at rest 100 m above the Earth’s surface.  It has a mass of 45 mg and a charge of -1.2 × 10-10 C.  The electric field between the cloud and the ground can be considered a uniform field with an electric field strength of 300 V m-1.  The surface of the Earth can be considered to be a positive plate. 

Calculate the change of electric potential energy of the raindrop as it falls to the ground as a percentage of the change of gravitational potential energy of the raindrop as it falls to the ground. 

4c2 marks

By considering your answer to part b), calculate the speed at which the rain drop hits the ground.

The effects of air resistance can be ignored in this question.

4d4 marks

Calculate the electric field strength which would be needed to prevent the raindrop from falling, and comment on the polarity of the Earth’s surface with respect to the cloud.

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5a2 marks

The uniform electric field between two conducting plates of potential difference 1400 V is shown in Figure 1. 

Figure 1

7-5-s-q--q5a-medium-aqa-a-level-physics

Draw three equipotential lines between the plates. Label the potential clearly for each line.

5b1 mark

Figure 2 shows part of the region around a small negative charge. 

Figure 2

7-5-s-q--q5b-medium-aqa-a-level-physics

The electric potential at point B due to this charge is –6.0 V. 

Calculate the electric potential at point A, due to the negative charge.

5c3 marks

Show that charge Q is –6.0 × 10–10 C. 

Express your answer to an appropriate number of significant figures.

5d3 marks

Calculate the work done when a +3.0 nC chargeis moved from point A to point C.

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