Fields in Physics

This page delves into the concept of fields in physics, focusing on scalar and vector fields. It provides clear definitions and explanations of these fundamental concepts, which are crucial for understanding many areas of physics.

A field is defined as a physical quantity (scalar or vector) determined at each point in a given space. The page distinguishes between scalar and vector fields:

Definition: A scalar field is defined by a value associated with a unit at each point in the considered space.

Definition: A vector field is defined by a vector (direction, sense, magnitude, and unit) at each point.

The concept of field lines is introduced for vector fields. Field lines are tangent to the field vector at each point and are oriented in the same direction as the vector.

The page then focuses on two specific types of fields: the electrostatic field and the gravitational field.

The electrostatic field, denoted as E, is created by an object with an electric charge. Its magnitude is given by the equation E = k × Q / d², where Q is the source charge and d is the distance from the charge.

Highlight: The electrostatic field depends only on the source charge and the distance from it, not on the test charge placed in the field.

Similarly, the gravitational field, denoted as g, is created by an object with mass. Its magnitude is given by the equation g = G × M / d², where M is the source mass and d is the distance from the mass.

Example: The Earth creates a gravitational field that affects objects near its surface, resulting in the familiar force of gravity.

Comparison of Electric and Gravitational Fields

This page provides a detailed comparison between electric and gravitational fields, highlighting their similarities and differences. It also introduces the concept of uniform fields, using the parallel plate capacitor as an example.

The electric field (E) and gravitational field (g) are compared side by side, showing their respective formulas, units, and vector representations:

• Electric field: E = k × Q / d² (N/C or V/m)
• Gravitational field: g = G × M / d² (N/kg)

Highlight: Both fields follow an inverse square law, with their strength decreasing as the square of the distance from the source increases.

The page illustrates the concept of field lines for both types of fields. For electric fields, the lines emanate from positive charges and terminate on negative charges. For gravitational fields, the lines always point towards the mass creating the field.

Example: The field lines around a positive charge point outward in all directions, while those around a negative charge point inward.

The special case of a uniform electric field is introduced using the parallel plate capacitor as an example. In this configuration, the electric field between the plates is constant in magnitude and direction.

Definition: A uniform field is characterized by parallel field lines of equal strength throughout the region.

The page concludes with a summary table comparing various aspects of electric and gravitational fields, including their sources, notations, units, and vector expressions. This comprehensive comparison helps solidify the understanding of these fundamental concepts in physics.