Consider a positive charge

q

and a negative charge

-q

, separated by a distance,

d

. The

z

-axis passes through both charges, and the origin,

z=0

, is at the midpoint between the two charges.\ a) Draw the configuration.\ b) Obtain a symbolic expression for the electric field at a point on the

z

-axis at arbitrary location,

z

. Express your answer in simplest form.\ c) Show that if

z>>d

the electric field is proportional to

(1)/(z^(3))

.\ d) What is the electric field at an arbitrary point on the line perpendicular to the

z

-axis that passes through

z=0

? You need a coordinate along this line, so let's call it

x

. How does this expression behave when

x>>d

?

Consider a positive charge q and a negative charge q, separated by a distance, d. The z-axis passes through both charges, and the origin, z=0, is at the midpoint between the two charges. a) Draw the configuration. b) Obtain a symbolic expression for the electric field at a point on the z-axis at arbitrary location, z. Express your answer in simplest form. c) Show that if z>>d the electric field is proportional to 1/z3. d) What is the electric field at an arbitrary point on the line perpendicular to the z-axis that passes through z=0 ? You need a coordinate along this line, so let's call it x. How does this expression behave when x>>d ? Consider a positive charge q and a negative charge q, separated by a distance, d. The z-axis passes through both charges, and the origin, z=0, is at the midpoint between the two charges. a) Draw the configuration. b) Obtain a symbolic expression for the electric field at a point on the z-axis at arbitrary location, z. Express your answer in simplest form. c) Show that if z>>d the electric field is proportional to 1/z3. d) What is the electric field at an arbitrary point on the line perpendicular to the z-axis that passes through z=0 ? You need a coordinate along this line, so let's call it x. How does this expression behave when x>>d