Electric Charges and Fields Physics Lesson 22 by Owen Borville 12.21.2025
Two types of electric charge exist: positive and negative. Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance. Most positive charges are carried by protons and most negative charges are carried by electrons. The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton. An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons. The SI unit for charge is the coulomb (C), with protons and electrons having opposite sign charges but equal magnitude. The magnitude of this charge | qe | is | qe | = 1.60 x 10-19 C.
When charge is created or destroyed, equal amounts of positive and negative are involved. Most often, existing charges are separated from neutral objects to obtain some net charge. Both positive and negative charges exist in neutral objects and can be separated by rubbing one object with another, causing electrons to be removed from bonds in one object and placed on another object, increasing the charge separation. For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons. The law of conservation of charge ensures that whenever a charge is created, an equal charge of the opposite sign is created at the same time, and the net charge of a closed system is constant.
Polarization is the separation of positive and negative charges in a neutral object. A conductor is a substance that allows charge to flow freely through its atomic structure. An insulator is an object that holds charge within its atomic structure. Objects with like charges repel each other, and objects with unlike charges attract each other. A conducting object is grounded if it is connected to the Earth through a conductor. Grounding allows transfer of charge to and from the earth's large reservoir. Objects can be charged by contact with another charged object and obtain the same sign charge. If an object is temporarily grounded, it can be charged by induction, and obtains the opposite sign charge. Polarized objects have their positive and negative charges concentrated in different areas, giving them a non-symmetrical charge and charge distribution. Polar molecules have an inherent separation of charge.
Charles Coulomb (1736-1806) published a mathematical equation that describes the electrostatic force between two objects. Coulomb's law reveals the magnitude of the force between point charges: F = k|q1q2|/r^2, where q1 and q2 are two point charges separated by a distance r, and k ≈ 8.99 x 10^9 N*m^2/C^2 The Coulomb force is very basic and fundamental, since most charges are due to point-like particles. The Coulomb force causes all electrostatic effects and most macroscopic forces. The Coulomb force is very strong compared to the gravitational force, another fundamental force. However, the Coulomb force can cancel because it can be either attractive or repulsive and gravitational force cannot cancel. The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles.
The electrostatic force field surrounding a charged object extends out into space in all directions. The electric field is an alteration of space caused by the electric charge, and the electric field mediates the electric force between a source charge and test charge. The electric field like the electric force obeys the superposition principle, where the total force on a charge from multiple sources is the vector sum of the individual forces from each source, and each force is calculated independently by Coulomb's law. The electrostatic force exerted by a point charge on a test charge at a distance r depends on the charge of both charges, as well as the distance between the two. The electric field E = F/q where F (QE) is the Coulomb or electrostatic force exerted on a small positive test charge q. E has units of N/C. The magnitude of the electric field E created by a point charge Q is E = k|Q|/r^2 where r is the distance from Q. The electric field E is a vector and fields due to multiple charges add like vectors. The electric field as a vector points away from positive charges and toward negative charges.
Many electric charges are continuous charge distributions, where the calculation of the field requires mathematical integration, such as one dimensional like a wire using a line charge density λ, two dimensional like a metal plate using surface charge density σ, and three dimensional like a metal sphere using volume charge density ρ. Source charge is a differential amount of charge dq. Calculating dq depends on the type of source charge distribution and symmetry of the charge distribution is important. A special case of these charge distributions includes the field of an infinite wire and the field of an infinite plane.
Electric field line drawings are useful visual tools for the field of a source charge. The properties of electric field lines for any charge distribution are (1) field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges. (2) the number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. (3) The strength of the field is proportional to the closeness of the field lines and it is proportional to the number of lines per unit area perpendicular to the lines. (4) the direction of electric field is tangent to the field line at any point in space. (5) Field lines can never cross.
Many molecules in living organisms are electrically charged, such as DNA. An uneven distribution of the positive and negative charges within a polar molecule produces a dipole. The effect of a Coulomb field generated by a charged object may be reduced or blocked by other nearby charged objects. Biological systems contain water and because water molecules are polar, they have a strong effect on other molecules in living systems.
If a permanent dipole is placed in an external electric field, it results in a torque that aligns it with the external field. If a nonpolar molecule or atom is placed in an external field, it gains an induced dipole that is aligned with the external field. The net field is the vector sum of the external field plus the field of the dipole physical or induced. The strength of the polarization is described by the dipole moment of the dipole, p (vector) = qd (vector). The torque on the dipole in the external E-field is τ (vector)= pE (vector)
A conductor allows free charges to move about within it. The electrical forces around a conductor will cause free charges to move around inside the conductor until static equilibrium is reached. Any excess charge will collect along the surface of a conductor. Conductors with sharp corners or points will collect more charge at those points. A lightning rod is a conductor with sharply pointed ends that collect excess charge on the building caused by an electric storm and allow it to dissipate back in to the air. Electrical storms result when the electrical field of Earth's surface in certain locations becomes more strongly charged, due to changes in the insulating effect of the air. A Faraday cage acts like a shield around an object, preventing electric charge from penetrating inside.
Electrostatics is the study of electric fields in static equilibrium. An addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink-jet printers, and electrostatic air filters.
Two types of electric charge exist: positive and negative. Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance. Most positive charges are carried by protons and most negative charges are carried by electrons. The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton. An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons. The SI unit for charge is the coulomb (C), with protons and electrons having opposite sign charges but equal magnitude. The magnitude of this charge | qe | is | qe | = 1.60 x 10-19 C.
When charge is created or destroyed, equal amounts of positive and negative are involved. Most often, existing charges are separated from neutral objects to obtain some net charge. Both positive and negative charges exist in neutral objects and can be separated by rubbing one object with another, causing electrons to be removed from bonds in one object and placed on another object, increasing the charge separation. For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons. The law of conservation of charge ensures that whenever a charge is created, an equal charge of the opposite sign is created at the same time, and the net charge of a closed system is constant.
Polarization is the separation of positive and negative charges in a neutral object. A conductor is a substance that allows charge to flow freely through its atomic structure. An insulator is an object that holds charge within its atomic structure. Objects with like charges repel each other, and objects with unlike charges attract each other. A conducting object is grounded if it is connected to the Earth through a conductor. Grounding allows transfer of charge to and from the earth's large reservoir. Objects can be charged by contact with another charged object and obtain the same sign charge. If an object is temporarily grounded, it can be charged by induction, and obtains the opposite sign charge. Polarized objects have their positive and negative charges concentrated in different areas, giving them a non-symmetrical charge and charge distribution. Polar molecules have an inherent separation of charge.
Charles Coulomb (1736-1806) published a mathematical equation that describes the electrostatic force between two objects. Coulomb's law reveals the magnitude of the force between point charges: F = k|q1q2|/r^2, where q1 and q2 are two point charges separated by a distance r, and k ≈ 8.99 x 10^9 N*m^2/C^2 The Coulomb force is very basic and fundamental, since most charges are due to point-like particles. The Coulomb force causes all electrostatic effects and most macroscopic forces. The Coulomb force is very strong compared to the gravitational force, another fundamental force. However, the Coulomb force can cancel because it can be either attractive or repulsive and gravitational force cannot cancel. The electrostatic force between two subatomic particles is far greater than the gravitational force between the same two particles.
The electrostatic force field surrounding a charged object extends out into space in all directions. The electric field is an alteration of space caused by the electric charge, and the electric field mediates the electric force between a source charge and test charge. The electric field like the electric force obeys the superposition principle, where the total force on a charge from multiple sources is the vector sum of the individual forces from each source, and each force is calculated independently by Coulomb's law. The electrostatic force exerted by a point charge on a test charge at a distance r depends on the charge of both charges, as well as the distance between the two. The electric field E = F/q where F (QE) is the Coulomb or electrostatic force exerted on a small positive test charge q. E has units of N/C. The magnitude of the electric field E created by a point charge Q is E = k|Q|/r^2 where r is the distance from Q. The electric field E is a vector and fields due to multiple charges add like vectors. The electric field as a vector points away from positive charges and toward negative charges.
Many electric charges are continuous charge distributions, where the calculation of the field requires mathematical integration, such as one dimensional like a wire using a line charge density λ, two dimensional like a metal plate using surface charge density σ, and three dimensional like a metal sphere using volume charge density ρ. Source charge is a differential amount of charge dq. Calculating dq depends on the type of source charge distribution and symmetry of the charge distribution is important. A special case of these charge distributions includes the field of an infinite wire and the field of an infinite plane.
Electric field line drawings are useful visual tools for the field of a source charge. The properties of electric field lines for any charge distribution are (1) field lines must begin on positive charges and terminate on negative charges, or at infinity in the hypothetical case of isolated charges. (2) the number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge. (3) The strength of the field is proportional to the closeness of the field lines and it is proportional to the number of lines per unit area perpendicular to the lines. (4) the direction of electric field is tangent to the field line at any point in space. (5) Field lines can never cross.
Many molecules in living organisms are electrically charged, such as DNA. An uneven distribution of the positive and negative charges within a polar molecule produces a dipole. The effect of a Coulomb field generated by a charged object may be reduced or blocked by other nearby charged objects. Biological systems contain water and because water molecules are polar, they have a strong effect on other molecules in living systems.
If a permanent dipole is placed in an external electric field, it results in a torque that aligns it with the external field. If a nonpolar molecule or atom is placed in an external field, it gains an induced dipole that is aligned with the external field. The net field is the vector sum of the external field plus the field of the dipole physical or induced. The strength of the polarization is described by the dipole moment of the dipole, p (vector) = qd (vector). The torque on the dipole in the external E-field is τ (vector)= pE (vector)
A conductor allows free charges to move about within it. The electrical forces around a conductor will cause free charges to move around inside the conductor until static equilibrium is reached. Any excess charge will collect along the surface of a conductor. Conductors with sharp corners or points will collect more charge at those points. A lightning rod is a conductor with sharply pointed ends that collect excess charge on the building caused by an electric storm and allow it to dissipate back in to the air. Electrical storms result when the electrical field of Earth's surface in certain locations becomes more strongly charged, due to changes in the insulating effect of the air. A Faraday cage acts like a shield around an object, preventing electric charge from penetrating inside.
Electrostatics is the study of electric fields in static equilibrium. An addition to research using equipment such as a Van de Graaff generator, many practical applications of electrostatics exist, including photocopiers, laser printers, ink-jet printers, and electrostatic air filters.