Download Phys 208 - Recitation E-Fields

Electric Fields - Phys 208
1. Fields from isolated charges
a. For the three arrangements of charges below, draw the electric field direction at each place where
a dot is located. Try to estimate the relative magnitudes of the field vectors. (All charges have the
same magnitude)
A
B
C
b. For the three arrangements of charges below, draw the electric field direction at each place where
a dot is located. Try to estimate the relative magnitudes of the field vectors.
A
B
C
2. Fields from continuous charges
2.1 A linear charge distribution.
There is an amount
of charge evenly distributed in a linear fashion.
x
L
a. If the length of the rod is , what will the linear charge density, , of the rod be?
b. What will the linear charge density be a section that is one-tenth the length of , i.e.
c. How much charge, call it
1/100 the length of ?
, (in terms of
?
and ) will there be on a section of the rod equal to
d. What will the electric field be due to that small bit of charge,
where the charge is located?
be, at a distance away from
e. Now, our goal is find the field at a point P(x,y), any where above this linear line of charge. To
make life easier, we'll say that point P lies on the x = 0 line, however, the center of the charged line
does not necessarily lie on this line. Knowing that the charge on a infinitesimal section dx, located
at point x, will be given given by:
, find the electric field at point P due to this
infinitesimal section. Your answer should contain , , , , and . Call this field
.
y
P
a
x=0
f. Now find
field.
b
and
, that is, the
x
and
components of this contribution to the total electric
g. Since these components are just the contributions from a small segment of the total linear charge,
we'll need to integrate over the length of the charged line to find the full contributions. Set up these
integrals for both the x component and the y component.
h. Considering the rod to extend from to , use these as the limits of integration and perform the
definite integrals to obtain expressions for the components of the electric field in and for our
point P.