Electric Potential (AQA A Level Physics)

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

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.

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

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

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

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

Figure 2

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.

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

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

Figure 2

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

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.

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

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.

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

Figure 1

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

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

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

Figure 3

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

Calculate the total electric potential at point P.

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 1000 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

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. 

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.

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.

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

Figure 1

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

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

Figure 2

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.

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

Express your answer to an appropriate number of significant figures.

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

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

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

Assume that the gold nucleus remains stationary during the collision.

The alpha particle is fired towards a polonium nucleus, which contains more protons than the gold nucleus. The  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.

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.

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

         E = - 

Where:

         Mass of the electron, 

         Radius of the orbit, r

         Magnitude of charge on an electron, e

         Permittivity of free space, ε₀

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.

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

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

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

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

Where:

• The distance r is the radius of an electron which is 2.82 fm

• e is the charge of an electron

• is the permittivity of free space

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

Figure 3

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

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

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, calculate the initial kinetic energy, in MeV, of each proton.

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.

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.

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.

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.

Another option to attack the second spacecraft is to create a superweapon which can be fired from their home planet.

As this weapon will be fired a long distance from the second spacecraft, the spaceship and shield can be modelled as a charged particle with 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 the shield stops them.

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.