ASSIGNMENT #3

**DUE ON SEPTEMBER 29, 2005**

**HAND-IN**

**CHAPTER #22:**

**QUESTIONS:**

**4
**Figure
22-23
shows two square arrays of charged particles. The squares, which are centered
on point *P*, are misaligned. The particles are separated by either *d*
or *d*/2 along the perimeters of the squares. What are the magnitude and
direction of the net electric field at *P*?

**PROBLEMS:**

••15 Figure 22-36
shows an uneven arrangement of electrons (e) and protons (p) on a circular arc
of radius *r* = 2.00 cm, with angles q_{1} = 30.0°, q_{ 2} =
50.0°, q_{
3} = 30.0°, and q_{
4} = 20.0°. What are the (a) magnitude and (b) direction (relative to the
positive direction of the *x* axis) of the net electric
field produced at the center of the arc?

••16 Figure 22-37
shows a plastic ring of radius *R* = 50.0 cm. Two small charged beads are
on the ring: Bead 1 of charge +2.00 mC is fixed in place at the left side;
bead 2 of charge +6.00 mC
can be moved along the ring. The two beads produce a net electric
field of magnitude *E* at the center of the ring. At what (a)
positive and (b) negative value of angle q should
bead 2 be positioned such that *E* = 2.00 × 10^{5} N/C?

••20 The electric field of an electric dipole
along the dipole axis is approximated by Equation 22-8
and Equation 22-9,
which result from the termination of the two binomial expansions shown just
before those equations. If the expansions were carried out further, what would
be the next nonzero term in the expression for the dipole's electric field
along the dipole axis? That is, what is *E*_{next}
in the expression

•••21 *Electric quadrupole.* Figure 22-39
shows an electric quadrupole. It consists of two dipoles
with dipole
moments that are equal in magnitude but opposite in direction. Show that the
value of *E* on the axis of the quadrupole for a
point *P* a distance *z* from its center (assume *z* *d*)
is given by

in which *Q* (= 2*qd*^{2})
is known as the *quadrupole** moment* of
the charge
distribution.

**ONLINE**

**CHAPTER #22:**

**QUESTIONS:**

**PROBLEMS:**

••10 In Figure 22-31,
the four particles are fixed in place and have charges *q*_{1} = *q*_{2}
= +5*e*, *q*_{3} = +3*e*, and *q*_{4} = –12*e*.
Distance *d* = 5.0 mm. What is the magnitude of the net electric
field at point *P* due to the particles?

••19 Figure 22-38 shows
an electric dipole. What are the (a) magnitude and (b) direction
(relative to the positive direction of the *x* axis) of the dipole's electric field
at point *P*, located at distance *r* *d*?

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