Electric potential

Flowers can attract bees by being colourful or by producing a scent. Some flowers also attract bees by producing an electric field.

When a bee gets close to a flower it can detect the electric field. The charge on the flower acts as a point charge at the centre of the flower.

At a distance of 0.06 m from the centre of a particular flower the potential is –16 V.

Show that the charge on this flower is about –0.1 nC.

The minimum field strength that a bee can detect is 120 V m^–1.

A teacher suggests that bees can detect the field when they are closer than 10 cm from the flower in (b)(i).

Deduce whether this suggestion is correct.

It is suggested that the hairs on a bee deflect slightly when close to the flower.

Explain what would cause a hair to deflect in an electric field.

Over one hundred years ago, Rutherford supervised a series of experiments using a source of alpha particles and thin gold foil.

Describe the model of the atom that Rutherford proposed as a result of this series of experiments.

The initial kinetic energy of an alpha (⁴₂α) particle is 7.310⁻¹³J.

In a textbook, it states that an alpha particle with this energy would be brought to rest when it reached a distance of 5.010⁻¹⁴m from the centre of the

Deduce whether this statement is correct.

Determine the initial momentum of the alpha particle.

An alpha particle moves along a path directly towards a gold nucleus, as shown.

An elastic interaction occurs and the alpha particle recoils.

State what is meant by an elastic interaction.

State what happens to the atoms in the gold foil as a result of these interactions.

The graph shows how the potential V varies with distance d in an electric field.

Which of the following shows the corresponding variation in electric field strength E?

A point object has a charge +Q.

Which of the following diagrams shows equipotential lines differing by a constant potential difference, and electric field lines around the object?

Questions 9 and 10 refer to the information below.

Alpha particle scattering investigations were first carried out in the early part of the 20th century.

9 An alpha particle with initial kinetic energy 8.810⁻¹³J approaches a nucleus of a gold (¹⁹⁷₇₉Au) atom. Which of the following is an equation for the closest distance r, in metres, between the alpha particle and the nucleus?

The diagram shows two parallel metal plates with a potential difference (p.d.) of 100 V across them. Three equipotential lines are shown.

Draw lines to represent the electric field in the shaded area.

A parallel plate capacitor consists of a thin layer of insulator of thickness d between two plates of conducting material of area A.

The capacitor has a capacitance 0.1 μF and is charged to a p.d. of 100 V by connecting it to an electrical supply.

The capacitor is then disconnected from the supply and the p.d. between the two plates slowly decreases. This is because the insulator is not perfect and a small charge can flow through it.

The graph shows how the p.d. varies with time.

The insulator is a type of plastic and should have a resistivity greater than 10¹⁴Ω m.

Deduce whether the plastic used in this capacitor has a resistivity greater than this value.

A = 5.6 10⁻³m²

d = 0.6 10⁻⁶m

At the beginning of the 20th century, Rutherford carried out large-angle alpha particle scattering experiments using gold (¹⁹⁷₇₉Au) foil. The vast majority of the alpha particles went straight through the foil whilst a few were deflected straight back.

Describe how the model of the atom changed, as a consequence of these experiments.

In one experiment the alpha particles had an initial energy of 7.7 MeV.

Calculate the distance of closest approach of the alpha particles to the nucleus of a gold atom. Assume that the gold nucleus remains at rest.

Rutherford also carried out the experiment with aluminium (₁₃²⁷Al) foil. The aluminium foil had the same thickness as the gold foil and the alpha particles had the same initial kinetic energy.

The following observations were made.

Observation 1: The fraction of alpha particles scattered at any particular angle for aluminium foil was always much less than for gold foil.

Observation 2: The alpha particles scattered from aluminium foil had less kinetic energy than the alpha particles scattered from gold foil.

Explain how these observations can be used to deduce how an aluminium nucleus compares to a gold nucleus.

The graph shows how an electric potential V varies with distance x.

Which of the following shows the corresponding variation of electric field strength E with x ?

The graph shows how an electric potential V varies with distance x.

Which of the following shows the corresponding variation of electric field strength E with x ?

The diagram shows a model used to demonstrate alpha particle scattering. A ball bearing is set rolling on a wooden track. The track is positioned so that the ball bearing rolls onto a metal sheet with a curved surface known as a ʻhillʼ.

The diagram shows a vertical cross-section through the hill. The surface is curved so that the height of a point h on the curved surface is inversely proportional to the distance r from the centre of the hill.

Explain why the hill is suitable as a model for the electric field surrounding the nucleus of an atom.

A plan view of the arrangement is shown.

The wooden track is moved to different positions and the ball bearing is released.

Describe the results of the alpha particle scattering experiment and how these can be demonstrated by moving the wooden track to different positions.

The diagram shows a model used to demonstrate alpha particle scattering. A ball bearing is set rolling on a wooden track. The track is positioned so that the ball bearing rolls onto a metal sheet with a curved surface known as a ʻhillʼ.

The diagram shows a vertical cross-section through the hill. The surface is curved so that the height of a point h on the curved surface is inversely proportional to the distance r from the centre of the hill.

Explain why the hill is suitable as a model for the electric field surrounding the nucleus of an atom.

A plan view of the arrangement is shown.

The wooden track is moved to different positions and the ball bearing is released.

Describe the results of the alpha particle scattering experiment and how these can be demonstrated by moving the wooden track to different positions.

State how the bee might use this to detect the electric field of a flower.

State the effect of a decreased electric field strength on the equipotential lines.

Sketch the electric field around a positive point charge.

A magician did a trick which he claimed was the most dangerous ever. He positioned himself midway between two charged spheres which were separated by a distance of about two metres. Each sphere was charged to a potential that would cause ionisation at a distance of one metre. He wore a protective suit of chain mail and a helmet consisting of a metal cage. The protective suit and helmet were earthed to a potential of 0 V.

A scientist said “there is no danger in this and I would happily do it tomorrow”.

Explain whether this statement is justified.

Our understanding of the atom has developed over time, from early models in which atoms were considered to be hard incompressible spheres, through to the nuclear model of the atom and the ladder model in which electrons exist in a discrete number of allowed energy states.

*(a) The model of atoms as hard incompressible spheres, moving rapidly and randomly, can be used to explain why gases exert a pressure.

Explain, using ideas of momentum, why the pressure exerted by a gas increases as the temperature of the gas increases.

The nuclear model of the atom was established following a series of experiments in which alpha particles were directed at thin gold foil.

An alpha particle approaching a gold nucleus,¹⁹⁷₇₉Au, head-on will be brought to rest and returned along its original path.

Calculate the minimum distance between the alpha particle and the nucleus for alpha particles of energy of 5.5 MeV.

It is observed that electrons, with energy of 5.5 keV, are diffracted as they pass through the thin gold foil.

Explain a conclusion about the electrons that can be made from this observation.

In the energy ladder model of the atom, electrons exist in a discrete number of allowed energy states. The collision of electrons with gold atoms may lead to the production of high frequency electromagnetic radiation.

Explain how high frequency electromagnetic radiation may be produced when electrons collide with atoms in a metal.

Motors usually have a rotating component which can do work W.

In the diagram below, electric field lines have been drawn around one pair of these spheres.

Add to the diagram to show • the directions of the field lines • the lines of equipotential.

The distance between the centres of each charged sphere in this pair is 5.0 cm.

Show that the force between this pair of charged spheres is about 0.04 N.

charge on each sphere = 0.10 μC

The table shows the typical power and the corresponding angular velocity required for three different appliances.

Deduce which of these appliances, in principle, could use the electrostatic motor in (b).

You should use the word equation in (a) and assume that the length of the rod in the electrostatic motor is 8.0 cm.

Assume that the electrostatic motor would deliver a constant force throughout one complete rotation.