Download Electric Charge, Forces and Fields Review Worksheet (Honors)

Electric Charge, Forces and Fields Review Worksheet (Honors)
1. A test charge of -5.0 x 10-7 C is placed between other charges so that it is 50 mm from a charge of -3.0 x 10-7 C and 10
cm from a charge of -6.0 x 10-7 C. The three charges lie along a straight line.
A) What is the magnitude and direction of the force on the test charge?
B) Where would the test charge have to be located in order to be in equilibrium?
2. According to a simplified model, the hydrogen atom consists of a proton circled by an electron orbiting at a radius of
5.2 x 10-11 m. How fast must an electron be moving if the required centripetal force is provided by the electric force
exerted by the proton?
3. Four charges of 1.0µC are located at the corners of a square with sides of 1.0 m per side.
A) What is the electric field at the center of the square (include direction)?
B) what is the electric field at the center of any side?
4.
A)
B)
C)
A particle carrying a charge of 10µC starts moving from rest in a uniform electric field whose magnitude is 50 N/C.
What is the force on the particle?
How much kinetic energy will the particle have after it has moved 1.0 m?
What is performing the work on the particle giving it this kinetic energy?
5. Two 3.0 g balloons are suspended by a nail by strings 50 cm long. Each balloon has a charge of +Q, and there is an
angle of 40° between the strings. What is Q?
6. Suppose the force between the Earth and Moon were electrical instead of gravitational, with the Earth having a positive
charge and the Moon having a negative one. If the magnitude of each charge were proportional to the respective body’s
mass, find the Q/m ratio required for the moon to follow its present orbit of 3.84 x 10 8 m radius with its period of 27.3
days. The Earth’s mass is 5.98 x 1024 kg, and the moon’s mass is 7.3 x 1022 kg.
7. Three charges of +q, +q, and –q are at the vertices of an equilateral triangle x m per side. Find the magnitude and
direction of the force on one of the positive charges.
8. You and a friend are reading a newspaper article about nuclear fusion energy generation in stars. The article describes
the helium nucleus, made up of two protons and two neutrons, as very stable so it doesn't decay. You immediately realize
that you don't understand why the helium nucleus is stable. You know that the proton has the same charge as the
electron except that the proton charge is positive. Neutrons you know are neutral. Why, you ask your friend, don't the
protons simply repel each other causing the helium nucleus to fly apart? Your friend says she knows why the helium
nucleus does not just fly apart. The gravitational force keeps it together, she says. Her model is that the two neutrons sit in
the center of the nucleus and gravitationally attract the two protons. Since the protons have the same charge, they are
always as far apart as possible on opposite sides of the neutrons. What mass would the neutron have if this model of the
helium nucleus works? Is that a reasonable mass? Looking in your physics book, you find that the mass of a neutron is
about the same as the mass of a proton and that the diameter of a helium nucleus is 3.0 x 10-13 cm.
9. You and a friend are doing the laundry when you unload the dryer and the discussion comes around to static
electricity. Your friend wants to get some idea of the amount of charge that causes static cling. You immediately take two
empty soda cans, which each have a mass of 120 grams, from the recycling bin. You tie the cans to the two ends of a
string (one to each end) and hang the center of the string over a nail sticking out of the wall. Each can now hangs straight
down 30 cm from the nail. You take your flannel shirt from the dryer and touch it to the cans, which are touching each
other. The cans move apart until they hang stationary at an angle of 10º from the vertical. Assuming that there are equal
amounts of charge on each can, you now calculate the amount of charge transferred from your shirt.
10. At each corner of a square of side l there are point charges of
magnitude Q, 2Q, 3Q, and 4Q (see figure over there) Determine the
force on
A) the charge 2Q due the other forces and
B) the magnitude and direction of the electric field in the center of the
square.
Q
l
2Q
l
4Q
3Q
Answers
1.
a) 0.27 N toward -6 x 10-7 C charge
b) x = 0.062 m from -3 x 10-7 C charge
2.
v = 2.205 x 106 m/s
3.
a) Electric field at the center = 0 (all charges cancel out)
b) Enet = 12,879 N/C directed out of one side
4.
a) F = 5 x 10-4 N in the same direction as field
b) KE = ΔW
W = F∙d
W = 5 x 10-4 J
c) The electric field is doing the work
5.
q = 7.95 x 10-7 C
6.
Not sure yet
7.
x – components same direction
Fnet = kq2/r2
8.
Assuming distance between each neutron and proton is ½ the distance between
the protons, the mass would have to be 9.29 x 10-10 kg which is 5.56 x 1017 times
larger then it is.
9.
Total charge transferred is 1.41 x 10-6 C
10.
a) 8.37kQ2/l2 @ 45˚ N of E
b) 5.66kq/l2 directed from the center bisecting the line between Q and 2Q
y – components cancel