 ## Gravitational Field, Electric Field and Magnetic Field

Comparative study between the Gravitational Field, Electric Field and Magnetic Field

 GRAVITATIONAL FIELD ELECTRIC FIELD MAGNETIC FIELD Source Body mass (punctual or mass distribution) Electric charge (punctual or mass distribution) Magnetic field variable in time Electric charge in motion – Electric current Electric field variable in time Force Proportional to the mass on which it acts   Attraction bioprofre | Gravitational Field | 01 Open and Incoming Proportional to the electrical charge on which it acts   Attraction or Repulsion bioprofre | Electric Field | 02 Open Incoming: -q Outgoing: +q Proportional to the electrical charge on which it acts   Attraction or Repulsion bioprofre | Magnetic Field | 03   Close (from N to S) Solenoidal field Features bioprofre | Gravitational Field, Electric Field and Magnetic Field | 04   Conservative It is a central field The work required to move a mass between two points of the field does NOT depend on the trajectory bioprofre | Gravitational Field, Electric Field and Magnetic Field | 07 bioprofre | Gravitational Field, Electric Field and Magnetic Field | 05 Conservative It is a central field The work required to move a mass between two points of the field does NOT depend on the trajectory bioprofre | Gravitational Field, Electric Field and Magnetic Field | 08 bioprofre | Gravitational Field, Electric Field and Magnetic Field | 06   Non Conservative It depends on the speed The work required to move a mass between two points of the field DOES depend on the trajectory BioProfe | Gravitational Field, Electric Field and Magnetic Field | 09

## Conservative Field

In a Conservative Field (Gravitational Field and Electric Field) the equipotential surface is the one which is integrated by all the points where the potential has a same determined value, existing different equipotential surfaces according to the value of the potential.

As it is deduced from Coulomb’s Law, the potential due to a punctual charge is given by the following formula: bioprofre | Gravitational Field, Electric Field and Magnetic Field | 10

From this formula it is deduced that the equipotential surfaces of the Electric Field created by a punctual charge are concentric spheres with the charge, since all their points are at the same distance, the radius of the charge, and therefore, the same potential: Bioprofe | Gravitational Field, Electric Field and Magnetic Field | 11

As seen in the drawing, the lines of force and the equipotential surfaces are perpendicular to each other. This shows that no work is done when moving a charge within the same equipotential surface: bioprofre | Gravitational Field, Electric Field and Magnetic Field | 12

And also: bioprofre | Gravitational Field, Electric Field and Magnetic Field | 13 Biorpofe | Gravitational Field, Electric Field and Magnetic Field | 14

In each of its points the line of force is tangent to the vector Field Intensity E, and, consequently, also to force F

## Non Conservative Field

In a Non-Conservative Field (Magnetic Field) there is no energy associated with the fixed points of the field, as the force of Field of Intensity of Velocity depends with the electric charge q that moves in its sine bioprofre | Gravitational Field, Electric Field and Magnetic Field | 15

This prevents that a potential function is defined that only depends on the position of the bodies in the Magnetic Field, that is, there is no associated potential energy that is retained when a particle moves within the field.