Fiveable
Fiveable

or

Log in

Find what you need to study


Light

Find what you need to study

3.11 Electric Charges and Fields

4 min readjanuary 6, 2023

K

Krish Gupta

Daniella Garcia-Loos

Daniella Garcia-Loos

K

Krish Gupta

Daniella Garcia-Loos

Daniella Garcia-Loos

Electric Charges and Fields

Electric Fields

An electric field is a vector field that describes the force experienced by a charged particle at a given point in space due to the presence of other charged particles.

Here are some key points about :

  • are created by electric charges, which can be either positive or negative. Positive charges create an electric field that points away from the charge, while negative charges create an electric field that points towards the charge.
  • The strength of an electric field is determined by the amount of charge producing the field and the distance from the charge. The electric field is stronger the closer you are to the charge and weaker the further away you are.
  • can be represented graphically using , which are lines that show the direction that a positive test charge would be pushed if placed in the field. The density of the lines indicates the strength of the field.
  • can be used to understand and analyze how electric forces and charges interact with each other.
  • are an important concept in and are used in a variety of applications, including electricity generation, motors and generators, and electronic devices.

Every charged object has an electric field surrounding it, similar to how every object with mass has its own gravitational field. The more charge (or mass) there is, the stronger the field is. The only difference is that, while a gravitational field must be attractive, an electric field can be either attractive or repulsive. By convention, we use the direction that a positive test charge will move to draw our .

Rules for Drawing:

  • Field lines are vectors and must be drawn with arrows.
  • Lines go away from a and towards a .
  • The strength of the field can be visually represented by the density of the field lines. Therefore field, lines must never touch or cross. This would represent an infinitely strong field.

Simple Fields

  • Point Charges
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-XrLEgHK2XQT7.png?alt=media&token=b8ddfa90-83d7-455a-9e2b-07b788cfd50f

Image from wikimedia.org

  • Two Point Charges
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-bek4P6UdiQKP.1?alt=media&token=9c356092-0624-4ace-8e73-f4e3a8ae7b51

Image from Ck12.org

  • Two Parallel Plates
  • Notice how the field is the same everywhere between the plates.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ttkR1jbjIzfh.png?alt=media&token=9d7c0fbf-6e7f-43bc-8ef6-5ec1bae14b6b

Image from researchgate.net

Try using the PhET simulation to create your own fields and notice the how the field strength changes as a function of charge and distance.

Electric Field Strength

We've seen visually what look like. Now it's time to mathematically describe them.

is a measure of the electric force experienced by a charged particle at a given point in space due to the presence of other charged particles.

Here are some key points about :

  • is represented by the symbol "E" and is measured in units of volts per meter (V/m).
  • The at a given point is determined by the amount of charge producing the field and the distance from the charge. The electric field is stronger the closer you are to the charge and weaker the further away you are.
  • can be calculated using the formula E = F/q, where E is the , F is the electric force experienced by the charged particle, and q is the charge of the particle.
  • is an important concept in and is used to understand and analyze how electric forces and charges interact with each other.
  • The at a point can be determined by measuring the force experienced by a charged particle placed at that point. The can also be calculated from the distribution of charges producing the field.

The basic idea is to place a test charge at various locations in the field, measure the electrostatic force at that location, then calculate the field strength. The equation off of your reference tables for is:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-z1dmItnDrRjr.PNG?alt=media&token=def6aeb1-4f6a-4b18-8a38-2bf6814c8d74

where Fe​ is the electrostatic force found by using , and q is the charge on the test charge used to measure the field.

We can also rearrange the equation to determine EE in terms of the charge on the point charge Q

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-a8NkT4EDAmaF.PNG?alt=media&token=8d784163-2d5c-4c1f-9786-10c54b0acfa8

Practice Questions

1.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fpractice%20question%201%203-beXCKlYIQ12i.png?alt=media&token=fa353401-2f55-46fe-a486-37d37560650c

Image created by author

Answer:

  • The force at each location is the same. The field is uniform so E is constant everywhere and q is the same for each case. Fe​=Eq, so the force must be the same.

2.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fpractice%20question%202%203-KuJZ1N40zznG.png?alt=media&token=5aee9659-d521-4901-9668-65816990a0d3

Image from apclassroom.collegeboard.org

At which of the labeled points on the x-axis is the electric field zero?

Answer:

  • Point A must have an of 0. The point must be closer to the smaller charge (Q) than the larger charge (-4Q), so it can't be D or E. It must also be where the force vectors between the test charge point in the opposite direction so that the net force is 0. Therefore, it can't be point C either. Since the (-4Q) is 4x greater than the , the point must be 2x as far from the -4Q charge as it is from the Q charge.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-FlYLiNFG0xJ7.PNG?alt=media&token=87d702ed-2e49-4c48-a4ac-bd837f11287f

That only leaves A as the answer.

3.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fpractice%20question%203%203-Atg2SxSCHB2T.png?alt=media&token=1e15ff2a-712d-43ba-b41d-882a5419364e

Image from apclassroom.collegeboard.org

Answer:

  • Graph A is correct. At x = 2 and x = 4, the distance from the charges is 0, so the field strength must trend towards infinity. At x = 3, the repulsion from the 2 charges cancels out so the field must be 0 there.

Key Terms to Review (8)

Coulomb's Law

: Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Electric Field Strength

: Electric field strength refers to the force experienced by a unit positive charge placed in an electric field. It quantifies how strong or weak an electric field is at any given point.

Electric Fields

: Electric fields are regions in space around charged objects where electric forces can be felt. They describe the influence that a charged object has on other charged objects in its vicinity.

Electromagnetism

: Electromagnetism refers to the branch of physics that deals with the interaction between electricity and magnetism. It explains how electric currents create magnetic fields and how changing magnetic fields can induce electric currents.

Lines of Force

: Lines of force refer to imaginary lines used to represent the direction and strength of electric fields around charged objects.

Negative Charge

: A negative charge refers to an object that has an excess of electrons, resulting in a net negative charge.

Positive Charge

: A positive charge refers to an object that has an excess of protons, resulting in a net positive charge.

Volts per Meter (V/m)

: Volts per meter (V/m) is the unit used to measure electric field strength. It represents the amount of electric potential difference (voltage) experienced by a charge placed at a distance of one meter from a source.

3.11 Electric Charges and Fields

4 min readjanuary 6, 2023

K

Krish Gupta

Daniella Garcia-Loos

Daniella Garcia-Loos

K

Krish Gupta

Daniella Garcia-Loos

Daniella Garcia-Loos

Electric Charges and Fields

Electric Fields

An electric field is a vector field that describes the force experienced by a charged particle at a given point in space due to the presence of other charged particles.

Here are some key points about :

  • are created by electric charges, which can be either positive or negative. Positive charges create an electric field that points away from the charge, while negative charges create an electric field that points towards the charge.
  • The strength of an electric field is determined by the amount of charge producing the field and the distance from the charge. The electric field is stronger the closer you are to the charge and weaker the further away you are.
  • can be represented graphically using , which are lines that show the direction that a positive test charge would be pushed if placed in the field. The density of the lines indicates the strength of the field.
  • can be used to understand and analyze how electric forces and charges interact with each other.
  • are an important concept in and are used in a variety of applications, including electricity generation, motors and generators, and electronic devices.

Every charged object has an electric field surrounding it, similar to how every object with mass has its own gravitational field. The more charge (or mass) there is, the stronger the field is. The only difference is that, while a gravitational field must be attractive, an electric field can be either attractive or repulsive. By convention, we use the direction that a positive test charge will move to draw our .

Rules for Drawing:

  • Field lines are vectors and must be drawn with arrows.
  • Lines go away from a and towards a .
  • The strength of the field can be visually represented by the density of the field lines. Therefore field, lines must never touch or cross. This would represent an infinitely strong field.

Simple Fields

  • Point Charges
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-XrLEgHK2XQT7.png?alt=media&token=b8ddfa90-83d7-455a-9e2b-07b788cfd50f

Image from wikimedia.org

  • Two Point Charges
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-bek4P6UdiQKP.1?alt=media&token=9c356092-0624-4ace-8e73-f4e3a8ae7b51

Image from Ck12.org

  • Two Parallel Plates
  • Notice how the field is the same everywhere between the plates.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ttkR1jbjIzfh.png?alt=media&token=9d7c0fbf-6e7f-43bc-8ef6-5ec1bae14b6b

Image from researchgate.net

Try using the PhET simulation to create your own fields and notice the how the field strength changes as a function of charge and distance.

Electric Field Strength

We've seen visually what look like. Now it's time to mathematically describe them.

is a measure of the electric force experienced by a charged particle at a given point in space due to the presence of other charged particles.

Here are some key points about :

  • is represented by the symbol "E" and is measured in units of volts per meter (V/m).
  • The at a given point is determined by the amount of charge producing the field and the distance from the charge. The electric field is stronger the closer you are to the charge and weaker the further away you are.
  • can be calculated using the formula E = F/q, where E is the , F is the electric force experienced by the charged particle, and q is the charge of the particle.
  • is an important concept in and is used to understand and analyze how electric forces and charges interact with each other.
  • The at a point can be determined by measuring the force experienced by a charged particle placed at that point. The can also be calculated from the distribution of charges producing the field.

The basic idea is to place a test charge at various locations in the field, measure the electrostatic force at that location, then calculate the field strength. The equation off of your reference tables for is:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-z1dmItnDrRjr.PNG?alt=media&token=def6aeb1-4f6a-4b18-8a38-2bf6814c8d74

where Fe​ is the electrostatic force found by using , and q is the charge on the test charge used to measure the field.

We can also rearrange the equation to determine EE in terms of the charge on the point charge Q

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-a8NkT4EDAmaF.PNG?alt=media&token=8d784163-2d5c-4c1f-9786-10c54b0acfa8

Practice Questions

1.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fpractice%20question%201%203-beXCKlYIQ12i.png?alt=media&token=fa353401-2f55-46fe-a486-37d37560650c

Image created by author

Answer:

  • The force at each location is the same. The field is uniform so E is constant everywhere and q is the same for each case. Fe​=Eq, so the force must be the same.

2.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fpractice%20question%202%203-KuJZ1N40zznG.png?alt=media&token=5aee9659-d521-4901-9668-65816990a0d3

Image from apclassroom.collegeboard.org

At which of the labeled points on the x-axis is the electric field zero?

Answer:

  • Point A must have an of 0. The point must be closer to the smaller charge (Q) than the larger charge (-4Q), so it can't be D or E. It must also be where the force vectors between the test charge point in the opposite direction so that the net force is 0. Therefore, it can't be point C either. Since the (-4Q) is 4x greater than the , the point must be 2x as far from the -4Q charge as it is from the Q charge.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-FlYLiNFG0xJ7.PNG?alt=media&token=87d702ed-2e49-4c48-a4ac-bd837f11287f

That only leaves A as the answer.

3.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2Fpractice%20question%203%203-Atg2SxSCHB2T.png?alt=media&token=1e15ff2a-712d-43ba-b41d-882a5419364e

Image from apclassroom.collegeboard.org

Answer:

  • Graph A is correct. At x = 2 and x = 4, the distance from the charges is 0, so the field strength must trend towards infinity. At x = 3, the repulsion from the 2 charges cancels out so the field must be 0 there.

Key Terms to Review (8)

Coulomb's Law

: Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Electric Field Strength

: Electric field strength refers to the force experienced by a unit positive charge placed in an electric field. It quantifies how strong or weak an electric field is at any given point.

Electric Fields

: Electric fields are regions in space around charged objects where electric forces can be felt. They describe the influence that a charged object has on other charged objects in its vicinity.

Electromagnetism

: Electromagnetism refers to the branch of physics that deals with the interaction between electricity and magnetism. It explains how electric currents create magnetic fields and how changing magnetic fields can induce electric currents.

Lines of Force

: Lines of force refer to imaginary lines used to represent the direction and strength of electric fields around charged objects.

Negative Charge

: A negative charge refers to an object that has an excess of electrons, resulting in a net negative charge.

Positive Charge

: A positive charge refers to an object that has an excess of protons, resulting in a net positive charge.

Volts per Meter (V/m)

: Volts per meter (V/m) is the unit used to measure electric field strength. It represents the amount of electric potential difference (voltage) experienced by a charge placed at a distance of one meter from a source.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.