Introductory Physics Volume Two

16 Electric Field 1.5
x/a = 0.0 0.5 1.0 1.5 2.0 2.5 3.0
y/a = 0.0 -90 -90 -90 -90 -90 -90 -90
0.5 -90 -54 -48 -52 -57 -61 -65
1.0 45 -3 -11 -20 -29 -36 -42
1.5 90 42 19 5 -7 -16 -23
2.0 90 61 39 23 11 1 -8
2.5 90 69 51 36 24 13 5
3.0 90 74 58 45 33 24 15
§ 1.4 Vector and Scalar Fields
Definition: Scalar Field
A scalar field is an entity that has a magnitude at each point in
space.
The potential energy is a scalar field, the quantity U = mgy gives
the amount of potential energy at each point (⃗r = xî+yĵ) in space.
Definition: Vector Field
A vector field is an entity that has a magnitude and direction at
each point in space.
Gravity is a vector field, the constant g = 9.8 m s
is the magnitude
2
of the field near the surface of the earth, and the direction is toward the
earth. If you move away from the surface of the earth the gravitational
field decreases in strength. The gravitational field is similar to the
electric field in the sense that they both give the force on a body. The
gravitational field gives the force on a massive body.
⃗F G = m⃗g
While, the electric field gives the force on a charged body.
⃗F E = q ⃗ E
Definition: Uniform Field
A uniform vector field is a vector field that has the same magnitude
and direction at all points in space. A uniform scalar field is a
scalar field that has the same value at all points in space.