Below is a ring of charged particles.
This ring of charge produces an electric field which can
be calculated by adding up the contributions to the field from
each piece of the ring.
The animation shows how this adding up (integration) process works
to produce the electric field along the axis through the center of the ring.
As the contribution of each part of the ring is added to the total, that
part of the ring is highlighted with red.
The electric field made by the highlighted portion is shown as a red
arrow while the sum of the red arrows is represented by the blue
arrow.
Notice that at the beginning of the process the electric field has
both vertical and sideways components.
As the process continues notice how the vertical component gets
bigger and bigger while the sideways component gradually diminishes
until at the end the field is only vertical.
This is the picture that goes with the integrals you did in Physics
122 and that we will be doing in class.