Gravitational and Electric Fields: Forces and Interactions
Item VIII. Gravitational and Electric Fields
These interaction forces between two bodies are given the name of contact forces.
However, there are many bodies that interact without touching. These interactions are explained by the concept of field.
8.1. Concept of Electric Field and Gravitational Field
The presence of an electric charge alters the space around it to produce an electric force on another charge nearby. Similarly, the presence of a mass alters the space around it so it produces a gravitational force on another body nearby.
The load mass and are surrounded by a field of influence on other bodies (gravitational field) on other charges (electric field).
- It is said that there is an electric field in a region of space where an electric charge placed at a point in this region experiences an electric force.
- It is said that there is a gravitational field in a region of space if a mass placed at a point in that region experiences a gravitational force.
8.1.1. Analogies Between the Electric Field and the Gravitational Field
Between the electric and gravitational fields, the following analogies can be established:
- Both fields are central because they are directed toward the point where the mass or load that creates them.
- They are conservative because the central force only depends on the distance.
- The central force that defines both fields is inversely proportional to the square of the distance.
Coulomb’s Law: The force of attraction or repulsion between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance that separates them.
The charges are scalar quantities that can be positive or negative.
Newton’s Law: Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance that separates them.
A central force is negative (attraction) if it is directed toward the center of the field and will be positive if it is directed outward (repulsive).
8.1.2. Differences Between the Gravitational Field and Electric Field
Although there are similarities between the two fields, there are differences that should be noted:
- The gravitational field is universal and exists for all bodies. The electric field exists only when bodies are charged with electricity.
- The gravitational field is always attractive, while the electric field can be either attractive (loads of different signs) or repulsive (like charges sign).
- The electric constant becomes K (1020) times the gravitational constant G. This indicates that the gravitational field is very weak compared with the electric field.
- A mass always creates a gravitational field. A moving electric charge, in addition to the electric field, also creates a magnetic field.
The unit of electric charge in SI is the coulomb. A coulomb is the charge passing through the cross-section of a conductor in a second when the intensity of current is one ampere.
8.2. Intensities of Gravitational and Electric Fields
If a particle creates a field, it only acts on those particles that possess the same property.
We call this characteristic particle body having the same properties as the body that created the field: If the field is gravitational, mass is characteristic; if the electric field is characteristic, it is the electrical charge.
The force per unit mass is the value of the gravitational field strength. The electric field strength is the force exerted by the field on a unit positive charge placed at a point.
The gravitational field strength vector is always directed toward the mass that creates it.
8.3. Law of Universal Gravitation
8.3.1. Kepler’s Laws
In 1609, Kepler enunciated the following empirical laws, confirming the ideas of Copernicus:
- Law of the Orbits: The planets orbit the Sun in elliptical orbits, describing one of whose foci is the Sun.
- Law of Areas: The areas swept by the radius vector from the Sun to a planet is directly proportional to the time employed. The velocity is constant.
- Law of Periods: The squares of the periods are directly proportional to the cubes of the semi-major axes of the respective orbits.
8.3.2. Derivation of the Law of Universal Gravitation
The acceleration of a planet is inversely proportional to the square of the radius of the orbit described.
Newton’s Law: Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
8.4. Coulomb’s Law
Coulomb’s law governs the interactions between two electric charges at rest. Coulomb’s law is defined as: the interaction force between two electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance that separates them.
8.5. Gravitational and Electrical Potential Energy
Potential energy in a central field point is the work done by the central force in moving the application point from infinity, where it is assumed that the force is zero, until that point.
Escape velocity is the speed that a body must acquire to escape the pull of the Earth.
Binding energy is the energy that a satellite must have to stay in orbit, circular stationary at a height h above the Earth. The lower the orbital radius, the greater the speed of the satellite should be.
8.6. Gravitational and Electrical Potential
Potential at a point in a field is the work done by the central force for moving the unit positive charge (or unit mass) under the action of the field from infinity, where we assume that the field is zero, to that point. The unit in the SI electrical potential is volt (July/coulomb)
Consequences of the gravitational potential:
- The potential at a point depends on the distance r from that point to the midfield. All points equidistant from the center of the field will have the same potential to form an equipotential surface.
- The electrical potential can be positive or negative, depending on the sign of charge Q that creates the field.
- The gravitational potential is always negative.
Potential difference between two points on a field is the work to move the unit positive charge (or unit mass) from each other point.
The gradient of potential is equal to the vector field strength of opposite sign.