1) You have a cylindrical metal shell of inner radius 6 cm and outer radius 9 cm. The shell has no net charge. Inside the shell is a line of charge of linear density of – 7 μC/m. Find the magnitude and direction of the electric field at (a) r = 3 cm, (b) r = 7 cm, and (c) r = 13 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.

. 1) You have a cylindrical metal shell of
inner radius 6 cm and outer radius 9 cm. The shell has no net charge. Inside the shell is a line of charge of linear density of – 7 μC/m. Find the magnitude and direction of the electric field at (a) r = 3 cm, (b) r = 7 cm, and (c) r = 13 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.
2) You have a uniformly charged
sphere of radius 5 cm and volume charge density of – 7 mC/m3. It is surrounded by a metal spherical shell with inner radius of 10 cm and outer radius of 15 cm. The shell has a net charge 8 μC. (a) Calculate the total charge on the sphere. Find the magnitude and direction of the electric field at (b) r = 13 cm and (c) r = 18 cm. Also, calculate the surface charge density of the shell on (d) the inner surface and (e) the outer surface.
3) Two 2 cm thick infinite slabs of metal are positioned as
shown in the diagram. Slab B has no net charge but Slab A has an excess charge of 5 μC for each square meter. The infinite plane at the origin has a surface charge density of – 8 μC/m2. Find the magnitude and direction of the electric field at (a) x = 2 cm, and (b) x = 4 cm. Also, calculate the surface charge density on (c) the left edge of A, (d) the right edge of A, and (e) the left edge of B.
4) A positive charge of 16 nC is nailed down with a #6 brad.
Point M is located 7 mm away from the charge and point G is 18 mm away. (a) Calculate the electric potential at Point M. (b) If you put a proton at point M, what electric potential energy does it have? (c) You release the
proton from rest and it moves to Point G. Through what potential difference does it move? (d) Determine the velocity of the proton at point G.
5)
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 of the net electric potential at point P.
6) Use the same charge distribution as in problem #5 but
change all odd-multiple charges to the opposite sign. Find the magnitude of the net electric potential at point P.
7) A parallel plate setup has a distance
between the plates of 5 cm. An electron is place very near the negative plate and released from rest. By the time it reaches the positive plate it has a velocity of 8 x 106 m/s. (a) As the electron moves between the plates what is the net work done on the charge? (b) What is the potential difference that the electron moves through? (c) What is the magnitude and direction of the electric field in between the plates?
– 8q +9q
– 4q
A B
0 3 cm 5 cm 8 cm 10 cm
+9q
– 5q
+6q+6q
+2q
P
+ M G
–
8)
A uniform line of charge with density, λ, and length, L is positioned so that its left end is at the origin. See diagram above. (a) Determine an equation (using integration) for the magnitude of the total electric potential at point P a distance, d, away from the origin. (b) Calculate the magnitude of the electric potential at P if d = 2 m, L = 1 m, and λ = – 5 μC/m. c) Using the equation you derived in part a), calculate the equation for the electric field at point P. It should agree with the result we got in Lecture Example #19.
9) You have a thin spherical shell
of radius 10 cm with a uni- form surface charge density of 11 μC/m2. Centered inside the sphere is a point charge of – 4 μC. Using integration, find the magnitude of the total electric potential at: (a) r = 16 cm and (b) r = 7 cm.
10) You have a uniformly
charged sphere of radius 5 cm and volume charge density of 6 mC/m3. It is surrounded by a metal spherical shell with inner radius of 10 cm and outer radius of 15 cm. The shell has no net charge. Find the magnitude of the electric potential at (a) r = 20 cm, (b) r = 12 cm, and (c) r = 8 cm.
11) Use the same physical situation with the exception
of changing the inner sphere to a solid metal with a surface charge density of 9 μC/m2 and giving the shell a net charge of – 3 μC. Find magnitude of the electric potential at (a) r = 20 cm, (b) r = 12 cm, (c) r = 8 cm, and (d) r = 2 cm.
12) CSUF Staff Physicist & Sauvé Dude, Steve
Marley, designs a lab experiment that consists of a vertical rod with a fixed bead of charge Q = 1.25 x 10–6 C at the bottom. See diagram. Another bead that is free to slide on the rod without friction has a mass of 25 g and charge, q. Steve releases the movable bead from rest 95 cm above the fixed bead and it gets no closer than 12 cm to the fixed bead. (a) Calculate the charge, q, on the movable bead. Steve then pushes the movable bead down to 8 cm above Q. He releases it from rest. (b) What is the maximum height that the bead reaches?
13)
d
P
0 – – – – –
L
You have two metal spheres each of diameter 30 cm that are space 20 cm apart. One sphere has a net charge of 15 μC and the other – 15 μC. A proton is placed very close to the surface of the positive sphere and is release from rest. With what speed does it hit the other sphere?
14) A thin spherical shell of radius, R, is centered at the
origin. It has a surface charge density of 2.6 C/m2. A point in space is a distance, r, from the origin. The point in space has an electric potential of 200 V and an electric field strength of 150 V/m, both because of the sphere. (a) Explain why it is impossible for r < R. (b) Determine the radius, R, of the sphere.
15) The two charges above are fixed and cannot move. Find a
point in space where the total electric potential will equal zero.