1) A charge of –1.5 μC is placed on the x axis at x = +0.55 m, while a charge of +3.5 μC is placed at the origin. (a) Calculate the magnitude and direction of the net electric field on the x-axis at x = +0.8 m. (b) Determine the magnitude and direction of the force that would act on a charge of –7.0 μC if it was placed on the x axis at x = +0.8 m.

1) A charge of –1.5 μC is placed on the x axis at
x = +0.55 m, while a charge of +3.5 μC is placed at the origin. (a) Calculate the magnitude and direction of the net electric field on the x-axis at x = +0.8 m. (b) Determine the magnitude and direction of the force that would act on a charge of –7.0 μC if it was placed on the x axis at x = +0.8 m.
2) For the same charge distribution of problem #1, do the
following. (a) Calculate the magnitude and direction of the net electric field on the x-axis at x = +0.4 m. (b) Determine the magnitude and direction of the force that would act on a charge of –7.0 μC if it was placed on the x axis at x = +0.4 m.
3)
Charges are placed at the three corners of a rectangle as shown. The charge values are q1 = 6 nC, q2 = – 4 nC, and q3 = 2.5 nC. Calculate the magnitude and direction of the electric field at the fourth corner.
4) For the same charge distribution of problem #3, with the
exception that you change both q1 and q2 to the opposite sign, calculate the magnitude and direction of the electric field at the fourth corner.
5) A drop of oil has a mass of 7.5 x 10–8 kg and a charge of
– 4.8 nC. The drop is floating close the to Earth’s surface because it is in an electric field. (a) Calculate the magnitude and direction of the electric field. (b) If the sign of the charge is changed to positive, then what is the acceleration of the oil drop? (c) If the oil drop starts from rest, then calculate the speed of the oil drop after it has traveled 25 cm.
6) A proton accelerates from rest in a uniform electric field
of magnitude 700 N/C. At a later time, its speed is 1.8 x 106 m/s. (a) Calculate the acceleration of the proton. (b) How much time is needed for the proton to reach this speed? (c) How far has the proton traveled during this time? (d) What is the proton’s kinetic energy at this time?
7) All the charges above are multiples of “q” where
q = 1μC. The horizontal and vertical distances between the charges are 25 cm. Find the magnitude and direction of the net electric field at point P.
8) Use the same charge distribution as in problem #7 but
change all even-multiple charges to the opposite sign. Find the magnitude and direction of the net electric field at point P.
9) In the above two diagrams, M & S, an electron is given an
initial velocity, vo, of 7.3 x 106 m/s in an electric field of 50 N/C. Ignore gravitation effects. (a) In diagram M, how far does the electron travel before it stops? (b) In diagram S, how far does the electron move vertically after it has traveled 6 cm horizontally? (Hint: Think projectile motion)
–+
+ P
q3 q2
q1
35 cm
20 cm
– 8q
– 4q
+9q
+9q
– 5q
+6q+6q
+2q
P
– vo – vo
S M
10) A 2 g plastic sphere is suspended by a 25 cm long piece of string. Do not ignore gravity. The sphere is hanging in a uniform electric field of magnitude 1100 N/C. See diagram. If the sphere is in equilibrium when the string makes a 20° angle with the vertical, what is the magnitude and sign of the net charge on the sphere?
11) You have an electric dipole of
opposite charges q and distance 2a apart. (a) Find an equation in terms of q, a, and y for the magnitude of the total electric field for an electric dipole at any distance y away from it. (b) Find an equation in terms of q, a, and y for the magnitude of the total electric field for an electric dipole at a distance y away from it for when y >> a.
12)
A dipole has an electric dipole moment of magnitude 4 μC·m. Another charge, 2q, is located a distance, d, away from the center of the dipole. In the diagram all variables of q = 20 μC and d = 80 cm. Calculate the net force on the 2q charge.
13) An electric dipole of charge 30 μC and separation 60 mm is put in a uniform electric field of strength 4 x 106 N/C. What is the magnitude of the torque on the dipole in a uniform field when (a) the dipole is parallel to the field, (b) the dipole is perpendicular to the field, and (c) the dipole makes an angle of 30º to the field. 20º
–
14) An electron of charge, – e, and mass, m, and a positron of
charge, e, and mass, m, are in orbit around each other. They are a distance, d, apart. The center of their orbit is halfway between them. (a) Name the force that is acting as the centripetal force making them move in a circle. (b) Calculate the speed, v, of each charge in terms of e, m, k (Coulomb’s Constant), and d.
+ y
–q
q
a
a
– + – q
d
q 2q +
15) A ball of mass, m, and positive charge, q, is dropped from
rest in a uniform electric field, E, that points downward. If the ball falls through a height, h, and has a velocity of
gh2v = , find its mass in terms of q, g, and E.
16)
+
6 cm
– – 4 μC 12 μC
The two charges above are fixed and cannot move. Find a
point in space where the total electric field will equal zero.