Introduction to Fields

History Action-at-a-distance - ie. a particle exerts a direct force on another particle even though these particles are not touching. This was suggested by Newton in his Law of Gravitation, yet even Newton had substantial misgivings about it

"it is inconceivable, that inanimate brute matter, should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact. That Gravity should be innate, inherent and essential to matter so that one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it."

According to the modern view, there is indeed an entity that conveys the force from one particle to another by contact. This entity is the FIELD.

Fields are a form of matter - they are endowed with energy and with momentum and they therefore exist in a material sense.

A FIELD is a property of space. An object(source) produces a field which in turn exerts a force on objects in the field

Consider a test charge, q t, much smaller than the source, producing a negligible field F=kqq t /r 2 - divide both sides by q t

F/q t = kq/r 2 notice that the right side depends only on the source charge and the distance to the point in space. There is no information about the object at point P. This provides a convenient way to describe the condition of space at point P.

left side is the Electric field Intensity or commonly the Electric Field, ε  ε =  F q /q

Gravitational fields g = F g /m this can be arranged to produce the familiar F=mg

Since magnetic monopoles don't exist, its not practical to try to define magnetic field intensities in a way that is similar to electric and gravitational fields.

Later, we’ll see that F b = I l B where F b is the force exerted by the magnetic field, I is current, l is length of conductor and B is magnetic field intensity B = F/I l The SI unit for magnetic field strength is the Tesla(T)

FIELDS NEAR POINT SOURCES ε =  F q /q is a general definition

We will also develop a formula for special cases, such as point charges ε = F q /q = kqq t /r 2 = kq/r 2 q t Why are the magnitude bars present?

Therefore, the electric field intensity near a point charge  │ ε │= kq/r 2 Likewise, │ g │= Gm s /r 2

FIELD LINES Electric Field Lines -lines representing a particle's motion if free to move in the field -at any point, the field is represented by a vector tangent to the field line -at any point, the motion of a positive test charge shows the direction of the field at that point

-field strength is represented by the density of lines - closely spaced lines --> stronger field -when more than one source charge is present, the electric field vector is the sum of the component field vectors see next diagram

Gravitational Field Lines -always attractive, so will resemble an electric field with negative charges

Magnetic Field Lines -In grade 11, we used a North Pole to find the field lines, but we know there is nothing such as a monopole -A more accurate and complete way of drawing field lines is to draw the line at a particular point in the direction the north pole of a compass at that position would point. -The # of field lines is called the magnetic flux

Things to remember: 1. Electrostatic force (Fq) and Electric Field Intensity(  ) are not the same thing! 2. Electrostatic force and Electric field intensity are both vectors and must be treated as such when dealing with multiple charges (component vectors) 3. magnetic forces are treated differently, since there are no monopoles 4.Field lines are a “representation” of the field -electric fields leave (+) and enter (–) -magnetic fields are loops-compass lines up, with north pointing in direction of field line -grav. fields are identical to (–) point charge