Electric fields and field strength

Ions orbit Jupiter in a ring called a plasma torus as shown in Figure 6. This question is about applying gravitational, magnetic and electric fields to a particle in the plasma.

An ion travels in a circular path at a speed of 74.2 km s⁻¹ and at a distance of 4.22 × 10⁸ m from the centre of Jupiter.

Student A suggests that the gravitational force acting on the ion due to Jupiter provides the centripetal acceleration of the ion.

Deduce whether this suggestion is correct.

Student B suggests that the magnetic field of Jupiter alone can cause the ion to move in the circular path.

Figure 7 shows the direction of the velocity v of the ion in the plasma torus. v is tangential to the plasma torus.

Figure 7

The ion has a positive charge.

Student B ’s suggestion requires a magnetic field to act at the position of the ion.

Draw an arrow on Figure 7 to show the direction of this magnetic field.

The ion has a charge of +3.20 × 10⁻¹⁹ C and a mass of 5.31 × 10⁻²⁶ kg.

The ion moves with a speed of 74.2 km s⁻¹ in a circle of radius 4.22 × 10⁸ m.

Calculate the magnitude of the magnetic flux density required for this motion. State, in fundamental (base) units, the unit for your answer. Ignore any contribution from the gravitational field.

The plasma torus contains two ions X and Y as shown in Figure 8. X has a charge of +2 e. Y has a charge of +1 e. Assume that each ion acts as a point charge.

Calculate the magnitude of the resultant electric field strength at point P in Figure 8 due to the two ions.

Two charged metal spheres have charges + Q and − q. The magnitude of + Q is greater than the magnitude of − q.

In which diagram are the electric field lines correct?

The diagram shows an electron in an electric field represented by equipotentials.

Which arrow shows the direction of the electric force on the electron?

The diagram shows point charges Q and q.

Q and q have charges of opposite sign.

The magnitude of the charge of Q is greater than the magnitude of the charge of q.

The electric field strength is zero at one of the points A, B, C or D.

At which point is the electric field strength zero?

The diagram shows two parallel conducting plates at potentials of −20 V and −10 V.

The displacement x is measured from the bottom (−20 V) plate.

Which graph shows how the electric field strength E varies with x ?

Which diagram shows a distribution of charge where the electric potential at P and the electric field at P are both zero?

An ion has a specific charge of −7.1 × 10⁷ C kg⁻¹. It is held stationary in a vertical electric field on the surface of the Earth.

What are the magnitude and direction of the electric field?

Figure 4 shows a spark detector used to detect alpha particles.

The detector consists of a metal mesh placed 5.0 mm above a wire. A potential difference of 4000 V is applied between the mesh and the wire.

Molecules in the air between the mesh and the wire are ionised by an alpha particle and a spark is produced.

Figure 5 shows equipotentials between the mesh and the wire.

Figure 5 shows a dashed line between the mesh and the wire.

Sketch on Figure 6 a graph to show how the magnitude E of the electric field strength varies with the distance d from the mesh along this dashed line. No values are required on the E axis.

An alpha particle passes through the mesh. The alpha particle ionises an argon atom at P on Figure 5, releasing one electron. The electron and the argon ion have no kinetic energy at P. The electron then travels to the wire and the argon ion travels to the mesh.

Assume that the air has no effect on the motion of the electron or on the motion of the argon ion.

mass of argon ion = 6.64 × 10⁻²⁶ kg

In practice, the air does affect the motion of the electron and the motion of the argon ion.

Suggest how the presence of air between the mesh and the wire changes the ratio in Question 04.2. No numerical detail is required.

The alpha source in Figure 4 is moved to different heights h above the mesh.

Figure 7 shows how the number of sparks N produced in 10 minutes varies with h. No sparks are produced when the source is not present.

Student A suggests that the spark rate obeys an inverse-square law. Student B suggests that the spark rate decreases exponentially with h.

Determine whether either student is correct.

Six metal spheres, each carrying a charge of magnitude Q, are equally spaced around a circle of diameter d.

What is the magnitude of the field strength at the centre of the circle?

The diagram shows the path of an electron in a uniform electric field. The electron moves in a vertical plane.

The direction of the electric field is

The diagram shows a uniform electric field of strength 15 V m. The length RS is perpendicular to the field and the line ST is parallel to the field.

What is the total change in electrical potential energy for a charge of 3.0 μC moving from R to T ?

Two parallel metal plates separated by a distance d have a potential difference V across them. A particle with charge Q is placed midway between the plates.

What is the magnitude of the electrostatic force acting on the particle?

An isolated spherical conductor is charged. The conductor has a radius R and an electric potential V. The electric field strength at its surface is E.

Point T is a distance 2 R from the surface.

What are the electric field strength and electric potential at T ?

Mass spectrometers are used to measure the masses of ions.

Figure 3 shows one part of a mass spectrometer.

A narrow beam consists of positive lithium ions travelling at different speeds. The beam enters a region where there is an electric field and a magnetic field. The directions of the uniform electric field of strength E and the uniform magnetic field of flux density B are shown on Figure 3.

Most ions are deflected from their original path. Lithium ions that travel at one particular speed are not deflected, and pass through the small aperture.

The positive lithium ion A in Figure 3 moves at a speed v.

Draw two labelled arrows on Figure 3 to show the directions of the electric force F_E and the magnetic force F_M acting on A.

Lithium ions travelling at 1.5 × 10⁵ m s⁻¹ pass through the small aperture.

Calculate E.

B = 0.12 T

Ions that pass through the small aperture enter a second uniform magnetic field of flux density B. Ions of different mass are separated because they follow different paths as shown in Figure 4.

Ions of mass m and charge q travelling at speed v follow a circular path in the uniform magnetic field.

Show that the radius r of the circular path is given by

The ions of different mass are deflected and strike the detector surface at different distances from the small aperture as shown in Figure 4.

A singly-charged lithium ion (⁶₃Li⁺) passes through the small aperture.

Calculate the distance between the small aperture and the point where this ion strikes the detector surface.

B = 0.12 T

Figure 5 shows a different type of mass spectrometer working with lithium ions.

A stationary⁷₃Li⁺ ion in the lithium sample is at the mid-point between the parallel electrodes. The⁷₃Li⁺ ion accelerates towards aperture P.

Determine the speed of the ion when it emerges through aperture P.

⁶Li⁺ Li⁷⁺ L ₃ and₃ ions are produced in the sample simultaneously and travel a distance from aperture P to the detector. For each type of ion, the time interval between production and detection is measured.

Discuss how the masses of the ions can be deduced from the measurement of these time intervals.

At a distance L from a fixed point charge, the electric field strength is E and the electric potential is V.

What are the electric field strength and the electric potential at a distance 3 L from the

A small object of mass m has a charge Q. The object remains stationary in an evacuated space between two horizontal plates. The plates are separated by a distance d and the potential difference between the plates is V.

What is V ?

An electric field acts into the plane of the paper. An electron enters the field at 90° to the field lines.

The force on the electron is

Define the electric field strength at a point in an electric field.

Figure 2 shows a point charge of +46 C placed 120 mm from a point charge Q.

Position P is on the line joining the charges at a distance 66 mm from charge Q. The resultant electric field strength at position P is zero.

Calculate the charge Q.

Explain, without calculation, whether net work must be done in moving a proton from infinity to position P in Figure 2.

A small rubber ball coated with a conducting paint carries a positive charge. The ball is suspended in equilibrium from a vertical wall by an uncharged non-conducting thread of negligible mass. The wall is positively charged and produces a horizontal uniform electric field perpendicular to the wall along the whole of its length. Figure 3 shows that the thread makes an angle of 30° to the wall.

The thread breaks.

Explain the motion of the ball.

A conducting sphere holding a charge of +10 C is placed centrally inside a second uncharged conducting sphere.

Which diagram shows the electric field lines for the system?

A charged spherical conductor has a radius r. An electric field of strength E exists at the surface due to the charge.

What is the potential of the spherical conductor?

An air-filled parallel-plate capacitor is charged from a source of emf. The electric field has a strength E between the plates. The capacitor is disconnected from the source of emf and the separation between the isolated plates is doubled.

What is the final electric field between the plates?

State what is represented by gravitational field lines.

Figure 6 shows the gravitational field above a small horizontal region on the surface of the Earth.

Suggest why the field lines converge over a small area at K.

A ball travelling at constant speed passes position J moving towards position K in Figure 6.

Assume friction is negligible.

Explain any change in the speed of the ball as it approaches K.

Figure 7 shows lines of force for the electric field surrounding two charged objects L and M.

Explain why the lines of force shown in Figure 7 cannot represent a gravitational field.

State which object L or M has a charge with the greater magnitude.

State which object L or M has a positive charge.

Draw, on Figure 7, an equipotential line that passes through point N. Do not extend your line beyond the given field lines.

Which graph best represents how the electric field strength E varies with the distance x in the space between the two plates?

What is the average acceleration of the particle?

What is the work done on the electron?