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4.1 Definition and Conservation of Electric Charge

7 min readjanuary 8, 2023

K

Krish Gupta

Daniella Garcia-Loos

Daniella Garcia-Loos

K

Krish Gupta

Daniella Garcia-Loos

Daniella Garcia-Loos

Definition and Conservation of Electric Charge

is a property of matter that causes it to feel a force in an electromagnetic field. must be conserved. The entire topic of and circuits is based upon the principle of conservation of charge. We learned about charge and its conservation in the last unit. In this unit, we will focus more on and how it relates to theconservation of charge.

In Unit 3, we studied and defined it as work per unit charge. There are 2 other important quantities used along with to describe the features of a circuit: and .

A common analogy for how , , and are related to each other is to think of an electric circuit like water flowing through a hose. is similar to the water pressure, is similar to the amount of water that gets through the hose, and is similar to mud or dirt that gets stuck in the hose and starts to clog it.

refers to the principle that the total in a closed system remains constant over time. This means that can be transferred or distributed within the system, but the total amount of charge remains the same.

Here are some key points about :

  • is a fundamental principle in physics and is a consequence of the law of conservation of mass-energy, which states that the total mass and energy of a closed system remains constant.
  • is a result of the symmetry of the laws of physics under charge conjugation, which is the transformation that changes all the charges in a system to their opposites (for example, changing all the positive charges to negative charges and vice versa).
  • is an important concept in electromagnetism and is used to understand and analyze the behavior of electric charges and electric fields.
  • can be used to predict the behavior of electric charges and electric circuits, including the flow of electric and the operation of batteries and generators.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3ssToOpTWVLy.png_ssl%3D1?alt=media&token=2c0140d0-4230-4cd0-ae66-b66ff42bc4e7

Image from freeingenergy.com

Current

is defined as the rate at which charge flows through a circuit. It's represented by the equation:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-OLZ4m2VwthPL.PNG?alt=media&token=e6088e80-0f15-4fdf-8461-a1e38ffa0717

where I is the (measured in Amps or milliAmps), Q is the charge passing a given point, and t is the time for the charge to pass through that point.

On a microscopic level, is also related to the (vd​) of the individual charge carriers. can be thought of as the average velocity of each charge carrier as it moves through a wire. In the image below, we're looking at the path of the electron as it moves through a wire.

is the average velocity of a charged particle, such as an electron, in an electric field. It is the velocity at which the charged particle would move if it were not subjected to any other forces or collisions.

Here are some key points about :

  • is usually very small compared to the speed of light, and it is typically measured in meters per second.
  • is determined by the strength of the electric field and the charge and mass of the charged particle. The stronger the electric field and the lighter the charged particle, the higher the .
  • is not the same as the speed of the charged particle. The charged particle may be moving at a much higher speed due to other forces and collisions, but its is the average velocity it would have if it were not subjected to these other forces.
  • is an important concept in electromagnetism and is used to understand and analyze the movement of charged particles in electric fields.
  • is related to the conductivity of a material. Materials with high conductivity have a high , which means that the charged particles can move through the material more easily. This makes the material a good conductor of electricity.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-wIq5FIbTerIK.jpg?alt=media&token=04b553ad-57fe-4386-82fd-19b3365bace8

Image from openstax.org

We can imagine that the in the wire would depend on the total number of charge carriers moving through the wire as well. A larger diameter wire would allow for more carriers. Combining these ideas together we can derive an equation for .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-wqGrGwXneh5W.png?alt=media&token=f4449956-4a41-48c1-ae68-49b774ac1ed6

Image from hyperphysics

Example Problem:

A metal wire has a cross-sectional area of 1 square millimeter and is subjected to an electric field of 1000 volts per meter. The wire is made of a metal with a of 1 millimeter per second for electrons. Calculate the electric flowing through the wire.

Solution:

To solve this question, you would need to use the formula for electric , which is I = qA vd, where I is the electric , q is the of the charged particles (in this case, electrons), A is the cross-sectional area of the wire, and vd is the of the charged particles. Using the given values, the electric flowing through the wire would be:

I = (1.6 x 10^-19 C) * (1 mm^2) * (1 mm/s) = 1.6 x 10^-19 C/s = 1.6 x 10^-15 A

Note that the electric is very small because the of the electrons is very small and the of an electron is also very small.

Circuit Symbols & Measuring Tools

To easily draw circuits, we use a variety of symbols to represent common components. Here are a few common ones, and there are many many more that are not used in AP 2 (although if you become an electrical engineer you'll use them!)

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-FO9r6u1w4djP.png?alt=media&token=7b72c0f6-b915-416f-b98a-55cbf2d90380

Image from wikimedia.org

There are also two tools listed in the image above: the and the . The is designed to accurately measure the potential difference between two points. Because of this, it is built with a very high internal so as not to create a short circuit when it bridges two points in a circuit. A is always connected in parallel around the object you are trying to measure.

On the other hand, an is designed to measure the flowing through a part of the circuit. Because it's going to be connected in series with the component it's measuring, the internal of the is designed to be very small. Hooking up an or in the wrong configuration can lead to short circuits or a meter that doesn't function at all. Be careful in your lab experiments, and check first before you connect them.

An is a device used to measure the electric flowing in a circuit, while a is a device used to measure the electric potential difference, or , across two points in a circuit.

Here are some key points about ammeters and voltmeters:

  • Ammeters are used to measure the electric flowing in a circuit. They are connected in series with the circuit and measure the flowing through the circuit.
  • Voltmeters are used to measure the , or electric potential difference, across two points in a circuit. They are connected in parallel with the circuit and measure the drop across the points being measured.
  • Ammeters and voltmeters are important tools in electrical engineering and are used to diagnose and troubleshoot problems in electrical systems.
  • Ammeters and voltmeters have different ranges and sensitivity, meaning they are designed to measure different ranges of and . It is important to use the appropriate meter for the measurement being taken.
  • Ammeters and voltmeters are usually part of a multimeter, which is a device that can measure multiple electrical quantities, including , , , and continuity.

    Key Terms to Review (11)

    Ammeter

    : An ammeter is a device used to measure the electric current flowing through a particular point in an electrical circuit.

    Ampere (A)

    : An ampere is the unit used to measure electric current. One ampere represents one coulomb of charge passing through a point in one second.

    Conservation of electric charge

    : Conservation of electric charge is a fundamental principle in physics that states that electric charge cannot be created or destroyed; it can only be transferred from one object to another. In other words, the total amount of positive and negative charges remains constant within an isolated system.

    Conventional Current

    : Conventional current refers to the assumed direction of flow of positive charges in an electrical circuit. It is the opposite direction to the actual movement of negatively charged electrons.

    Coulomb (C)

    : The coulomb is the unit of electric charge in the International System of Units (SI). It represents the amount of electric charge transported by a constant current of one ampere in one second.

    Current

    : Current refers to the flow of electric charge in a circuit. It is measured in Amperes (A) and represents the rate at which charges move through a conductor.

    Drift Velocity

    : The drift velocity is the average velocity of charged particles, such as electrons, in a conductor when an electric field is applied. It represents the net motion of charges due to the electric field.

    Electric Charge

    : Electric charge refers to the fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It can be positive or negative.

    Resistance

    : Resistance is a measure of how much an object or material opposes the flow of electric current. It determines how difficult it is for electrons to move through a circuit.

    Voltage

    : Voltage refers to the electric potential difference between two points in an electrical circuit. It represents the amount of energy that each unit of charge possesses.

    Voltmeter

    : A voltmeter is a device used to measure the voltage or potential difference between two points in an electrical circuit.

    4.1 Definition and Conservation of Electric Charge

    7 min readjanuary 8, 2023

    K

    Krish Gupta

    Daniella Garcia-Loos

    Daniella Garcia-Loos

    K

    Krish Gupta

    Daniella Garcia-Loos

    Daniella Garcia-Loos

    Definition and Conservation of Electric Charge

    is a property of matter that causes it to feel a force in an electromagnetic field. must be conserved. The entire topic of and circuits is based upon the principle of conservation of charge. We learned about charge and its conservation in the last unit. In this unit, we will focus more on and how it relates to theconservation of charge.

    In Unit 3, we studied and defined it as work per unit charge. There are 2 other important quantities used along with to describe the features of a circuit: and .

    A common analogy for how , , and are related to each other is to think of an electric circuit like water flowing through a hose. is similar to the water pressure, is similar to the amount of water that gets through the hose, and is similar to mud or dirt that gets stuck in the hose and starts to clog it.

    refers to the principle that the total in a closed system remains constant over time. This means that can be transferred or distributed within the system, but the total amount of charge remains the same.

    Here are some key points about :

    • is a fundamental principle in physics and is a consequence of the law of conservation of mass-energy, which states that the total mass and energy of a closed system remains constant.
    • is a result of the symmetry of the laws of physics under charge conjugation, which is the transformation that changes all the charges in a system to their opposites (for example, changing all the positive charges to negative charges and vice versa).
    • is an important concept in electromagnetism and is used to understand and analyze the behavior of electric charges and electric fields.
    • can be used to predict the behavior of electric charges and electric circuits, including the flow of electric and the operation of batteries and generators.

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-3ssToOpTWVLy.png_ssl%3D1?alt=media&token=2c0140d0-4230-4cd0-ae66-b66ff42bc4e7

    Image from freeingenergy.com

    Current

    is defined as the rate at which charge flows through a circuit. It's represented by the equation:

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-OLZ4m2VwthPL.PNG?alt=media&token=e6088e80-0f15-4fdf-8461-a1e38ffa0717

    where I is the (measured in Amps or milliAmps), Q is the charge passing a given point, and t is the time for the charge to pass through that point.

    On a microscopic level, is also related to the (vd​) of the individual charge carriers. can be thought of as the average velocity of each charge carrier as it moves through a wire. In the image below, we're looking at the path of the electron as it moves through a wire.

    is the average velocity of a charged particle, such as an electron, in an electric field. It is the velocity at which the charged particle would move if it were not subjected to any other forces or collisions.

    Here are some key points about :

    • is usually very small compared to the speed of light, and it is typically measured in meters per second.
    • is determined by the strength of the electric field and the charge and mass of the charged particle. The stronger the electric field and the lighter the charged particle, the higher the .
    • is not the same as the speed of the charged particle. The charged particle may be moving at a much higher speed due to other forces and collisions, but its is the average velocity it would have if it were not subjected to these other forces.
    • is an important concept in electromagnetism and is used to understand and analyze the movement of charged particles in electric fields.
    • is related to the conductivity of a material. Materials with high conductivity have a high , which means that the charged particles can move through the material more easily. This makes the material a good conductor of electricity.

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-wIq5FIbTerIK.jpg?alt=media&token=04b553ad-57fe-4386-82fd-19b3365bace8

    Image from openstax.org

    We can imagine that the in the wire would depend on the total number of charge carriers moving through the wire as well. A larger diameter wire would allow for more carriers. Combining these ideas together we can derive an equation for .

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-wqGrGwXneh5W.png?alt=media&token=f4449956-4a41-48c1-ae68-49b774ac1ed6

    Image from hyperphysics

    Example Problem:

    A metal wire has a cross-sectional area of 1 square millimeter and is subjected to an electric field of 1000 volts per meter. The wire is made of a metal with a of 1 millimeter per second for electrons. Calculate the electric flowing through the wire.

    Solution:

    To solve this question, you would need to use the formula for electric , which is I = qA vd, where I is the electric , q is the of the charged particles (in this case, electrons), A is the cross-sectional area of the wire, and vd is the of the charged particles. Using the given values, the electric flowing through the wire would be:

    I = (1.6 x 10^-19 C) * (1 mm^2) * (1 mm/s) = 1.6 x 10^-19 C/s = 1.6 x 10^-15 A

    Note that the electric is very small because the of the electrons is very small and the of an electron is also very small.

    Circuit Symbols & Measuring Tools

    To easily draw circuits, we use a variety of symbols to represent common components. Here are a few common ones, and there are many many more that are not used in AP 2 (although if you become an electrical engineer you'll use them!)

    https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-FO9r6u1w4djP.png?alt=media&token=7b72c0f6-b915-416f-b98a-55cbf2d90380

    Image from wikimedia.org

    There are also two tools listed in the image above: the and the . The is designed to accurately measure the potential difference between two points. Because of this, it is built with a very high internal so as not to create a short circuit when it bridges two points in a circuit. A is always connected in parallel around the object you are trying to measure.

    On the other hand, an is designed to measure the flowing through a part of the circuit. Because it's going to be connected in series with the component it's measuring, the internal of the is designed to be very small. Hooking up an or in the wrong configuration can lead to short circuits or a meter that doesn't function at all. Be careful in your lab experiments, and check first before you connect them.

    An is a device used to measure the electric flowing in a circuit, while a is a device used to measure the electric potential difference, or , across two points in a circuit.

    Here are some key points about ammeters and voltmeters:

  • Ammeters are used to measure the electric flowing in a circuit. They are connected in series with the circuit and measure the flowing through the circuit.
  • Voltmeters are used to measure the , or electric potential difference, across two points in a circuit. They are connected in parallel with the circuit and measure the drop across the points being measured.
  • Ammeters and voltmeters are important tools in electrical engineering and are used to diagnose and troubleshoot problems in electrical systems.
  • Ammeters and voltmeters have different ranges and sensitivity, meaning they are designed to measure different ranges of and . It is important to use the appropriate meter for the measurement being taken.
  • Ammeters and voltmeters are usually part of a multimeter, which is a device that can measure multiple electrical quantities, including , , , and continuity.

    Key Terms to Review (11)

    Ammeter

    : An ammeter is a device used to measure the electric current flowing through a particular point in an electrical circuit.

    Ampere (A)

    : An ampere is the unit used to measure electric current. One ampere represents one coulomb of charge passing through a point in one second.

    Conservation of electric charge

    : Conservation of electric charge is a fundamental principle in physics that states that electric charge cannot be created or destroyed; it can only be transferred from one object to another. In other words, the total amount of positive and negative charges remains constant within an isolated system.

    Conventional Current

    : Conventional current refers to the assumed direction of flow of positive charges in an electrical circuit. It is the opposite direction to the actual movement of negatively charged electrons.

    Coulomb (C)

    : The coulomb is the unit of electric charge in the International System of Units (SI). It represents the amount of electric charge transported by a constant current of one ampere in one second.

    Current

    : Current refers to the flow of electric charge in a circuit. It is measured in Amperes (A) and represents the rate at which charges move through a conductor.

    Drift Velocity

    : The drift velocity is the average velocity of charged particles, such as electrons, in a conductor when an electric field is applied. It represents the net motion of charges due to the electric field.

    Electric Charge

    : Electric charge refers to the fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It can be positive or negative.

    Resistance

    : Resistance is a measure of how much an object or material opposes the flow of electric current. It determines how difficult it is for electrons to move through a circuit.

    Voltage

    : Voltage refers to the electric potential difference between two points in an electrical circuit. It represents the amount of energy that each unit of charge possesses.

    Voltmeter

    : A voltmeter is a device used to measure the voltage or potential difference between two points in an electrical circuit.


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    © 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.