Social networks

OpenProf

Unlock access to content

Select one option:

Free of charge

Unlock the chapter "Uniform Electric Fields and Field Lines"

Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »

Subscribe to OpenProf If you do not get a better grade, you get your money back!

Unlock access to all problems solutions.
Available from 8.25 £ / month.

Continue »

Solved problems for the chapter:

Uniform Electric Fields and Field Lines

View the theory »

Motion of a Charged Particle in an Electric Field

1. Acceleration of an electrically charged particle in an electric field

2. Velocity and distance of an electrically charged particle while moving in an electric field

2.1. Linear motion

2.2. Planar motion

3. Energy of a particle in an electric field

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:uniform_electric_fields_and_field_lines/4396/

Example 1.

The electrical potential energy of an electron increases by 4 keV. How much voltage does it use?

Example 2.

An Electron and a proton move in the direction of the lines of force of a homogeneous electric field. What are their accelerations? The strength of the electric field is 10 kV/cm.

The base charge of an electron is , the mass of an electron is and the mass of a proton is .

An electron flies at an initial speed of 20,000 km/s into a homogeneous electric field of density 1 kV/cm. The direction of motion of the electron is the same as the direction of the electric field lines.

At what distance does the electron stop?
How does it move thereafter?

The charge of an electron is and the mass is .

Two oppositely charged parallel plates are spaced 2 cm apart. A proton is at rest next to the positively charged plate. We connect a voltage of 40 kV across the plates so that the proton starts to move towards the negatively charged plate. How long does it take to reach it?

The base charge of a proton is , and the mass of the proton is .

A stream of electrons flows through the cathode ray tube from left to right and hits the screen there. A sawtooth voltage with an amplitude of 20 V and an oscillation period of 1.1 s acts on the stream. Sawtooth plate electrodes are placed vertically and deflect the electrons perpendicular to their direction of motion. A voltage of 2 V deflects the stream on the screen by 1 cm. The voltage range from one side of the screen to the other is from -10 V to +10 V. How long does it take for the spot of the stream to travel the distance of 1 cm on the screen?

Two parallel plates of length 8 cm each are spaced 3 mm apart. The plates are connected to an electrical voltage. An electron flies between the plates at a speed of 80,000 km/s so that upon entering, the track of its motion is parallel to the plates and is located next to the negatively charged plate. What is the voltage between the plates so that the electron will just hit the positively charged plate after the flight?

The charge of an electron is and the mass is .

An electron flies in between two horizontal parallel plates at a speed of 12000 km/s and at an angle with respect to the horizontal. The upper plate is negatively charged while the lower one is positively charged. What is the voltage between the plates if the electron exits at an angle . The length of the plates is 10 cm and the distance between them is 8 mm.

The charge of the electron is and the mass of the electron is .

A moving proton enters the region between the plates from the left, as shown in the figure below.

The proton is deflected by the electric field. On the figure above, draw a line to show the path of the proton as it moves through and out of the region of the electric field.
A helium nucleus now enters the region of the electric field along the same initial path as the proton and travelling at the same initial speed. State and explain how the final speed of the helium nucleus compares with the final speed of the proton after leaving the region of the electric field.

By reference to electric field lines, explain why, for points outside an isolated spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre.

10.

State what is meant by a field of force.
State what is indicated by the direction of an electric field line.

11.

Two isolated protons are separated in a vacuum by a distance .

Calculate the ratio
By reference to your answer in (a), suggest why gravitational forces are not considered when calculating the force between charged particles.

12.

The figure below shows a pair of parallel metal plates with a potential difference (p.d.) of between them.

The plates are separated by a distance of . The plates are in a vacuum.

On the figure, draw five lines to represent the electric field in the region between the plates.
Calculate the strength of the electric field between the plates.

13.

State one similarity and one difference between the fields of force produced by an isolated point charge and by an isolated point mass.

14.

Two horizontal metal plates are separated by a distance of in a vacuum. A potential difference of is maintained between the plates, as shown in the figure below.

A proton is in the space between the plates. Explain quantitatively why, when predicting the motion of the proton between the plates, the gravitational field is not taken into consideration.

15.

A metal sphere of radius is isolated in space. Point P is a distance from the centre of the sphere, as illustrated in the figure below.

The variation with distance of the electric field strength due to the charge on the sphere is shown in the graph below.

An -particle is situated a distance from the centre of the sphere. Calculate the acceleration of the -particle.

16.

Define electric field.
State one similarity and one difference between the gravitational potential due to a point mass and the electric potential due to a point charge.

17.

For any point outside a spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre. By reference to electric field lines, explain this.

18.

State how the direction of the electric field at the surface of the Earth compares with the direction of the gravitational field.

19.

State what is meant by a line of force in an electric field.
A charged metal sphere is isolated in space. State one similarity and one difference between the gravitational force field and the electric force field around the sphere.

20.

State one similarity and one difference between the electric field lines and the gravitational field lines around an isolated positively charged metal sphere.

21.

An -particle is emitted from a radioactive source with kinetic energy of . The -particle travels in a vacuum directly towards a gold nucleus, as illustrated in the figure below.

The -particle and the gold nucleus may be considered to be point charges in an isolated system. For the closest approach of the -particle to the gold nucleus, determine

their separation,
the magnitude of the force on the -particle.

22.

A positive point charge is positioned at a fixed point X and an identical positive point charge is positioned at a fixed point Y, as shown in the figure below.

The charges are separated in a vacuum by a distance of . Points A and B are on the line XY. Point A is a distance of from X and point B is a distance of from Y. The electric field strength at point A is .

A small positive charge is placed at A. The electric field causes this charge to move from rest along the line AB. Describe the acceleration of the charge as it moves from A to B.

23.

An electron enters the region between two parallel plates P and Q, that are separated by a distance of , as shown in the figure below.

State the direction of the electric force on the electron when between the plates.
Explain why the electron does not follow a circular path.

24.

State what is meant by an electric field.

25.

State what is represented by an electric field line.

26.

State a similarity between the gravitational field lines around a point mass and the electric field lines around a point charge.

27.

An electron enters the region between two parallel plates P and Q, that are separated by a distance of , as shown in the figure below.

The space between the plates is a vacuum. The potential difference between the plates is . The electric field may be assumed to be uniform in the region between the plates and zero outside this region. Determine the magnitude of the force acting on the electron due to the electric field.