Download 2011 Take Home Electric Field Gauss` Law AP

2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
Name_________________
Score_____/
1. The following collection of point charges is assembled in space in the arrangement
shown below. Find the net force on Q3. Let Q1=Q2=Q3=10C. Each side of the square
is 1.00m.
Q1
Q2
Q3
2. An alpha particle is projected into an electric field as shown below (not to scale)
v= 2.0 x 106 m/s, m=6.68 x 10-27 kg, q=3.2 x 10-19 C, E= 500 N/C(-j)
a. The particle is in the field for precisely 10cm horizontally. Find the velocity of
the particle (use i and j notation)when it leaves the field.
b. Determine the distance that the particle is deflected when it leaves the field.
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
3.
a.
A wall has a negative charge distribution producing a uniform horizontal electric field. A small plastic ball
of mass 0.01 kg, carrying a charge of -80.0 C, is suspended by an uncharged, nonconducting thread 0.30
m long. The thread is attached to the wall and the ball hangs in equilibrium, as shown above, in the electric
and gravitational fields. The electric force on the ball has a magnitude of 0.032 N.
On the diagram below, draw and label the forces acting on the ball.
b.
Calculate the magnitude of the electric field at the ball's location due to the charged wall, and state its direction
relative to the coordinate axes shown.
c.
Determine the perpendicular distance from the wall to the center of the ball.
d.
The string is now cut.
i. Calculate the magnitude of the resulting acceleration of the ball, and state its direction relative to the
coordinate axes shown.
ii.
Describe the resulting path of the ball.
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
4.
a.
A charge Q1 = -1.6 x 10-6 coulomb is fixed on the x-axis at +4.0 meters, and a charge
Q2 = + 9 x 10-6 coulomb is fixed on the y-axis at +3.0 meters, as shown on the diagram above.
i. Calculate the magnitude of the electric field E1 at the origin O due to charge Q1
ii. Calculate the magnitude of the electric field E2 at the origin O due to charge Q2.
iii. On the axes below, draw and label vectors to show the electric fields E1 and E2 due to each charge,
and also indicate the resultant electric field E at the origin.
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
A charge Q3 = -4 x 10-6 coulomb is brought from a very distant point by an external force and placed at the origin.
c. On the axes below, indicate the direction of the force on Q3 at the origin.
5.
a.
Two point charges, Q1 and Q2, are located a distance 0.20 meter apart, as shown above. Charge Q 1 =
+8.0C. The net electric field is zero at point P, located 0.40 meter from Q 1 and 0.20 meter from Q2.
Determine the magnitude and sign of charge Q2.
b.
Determine the magnitude and direction of the net force on charge Q 1
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
6.
Find the electric field due to the two charges below at point P.
-Q
x
a
a
P
-Q
a. Draw the direction of the electric field at point P.
b. Find the magnitude of the electric field at point P in terms of k, x, a and Q.
7. Find the electric field at point C which is at the center of curvature for the two curved
rods below. The left rod has total charge +q, while the right (bold) rod has total charge 2q.
C
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
8.
A ring of radius a has a total charge +Q distributed uniformly around its circumference. As shown in
Figure I, the point P is on the axis of the ring at a distance b from the center of the ring.
a. Find the electric field at b=0. Why?
b. On the figure above show the direction of the electric field at point P
c. Find the magnitude of the electric field at P in terms of k, a, b, and +Q. Show
integration!!!!!!
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
9.
A spherical conducting shell has a charge of 14C on its outer
surface and a charged particle in its hollow. If the net charge on the shell is –10C,
what is the charge
a. on the inner surface?
b. of the particle?
10.
The electric field everywhere on the surface of a thin spherical shell
of radius 0.750 m is measured to be 890 N/C and points radially toward the center of the
sphere. What is the net charge within the sphere’s surface?
11. A nonconducting sphere with center C and radius a
has a spherically symmetric electric charge density.
The total charge of the object is Q> 0.
a. Determine the magnitude and direction of the electric field
at point P, which is a distance R> a to the right of the
sphere's center.
b. Determine the flux of the electric field through the spherical surface centered at C and passing
through P.
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
A point particle of charge -Q is now placed a distance R below point
P. as shown above.
c. Determine the magnitude and direction of the electric field at point
P
12.
A long straight wire is surrounded by a hollow metal cylinder whose
axis coincides with that of the wire. The wire has a charge per unit length of , and the
cylinder has a net charge per unit length of 2.
a. Draw a sketch of the situation
b. Use Gauss’ Law to find the electric field between the wire and the cylinder.
c. Use Gauss’ Law to find the electric field outside the cylinder.
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
13.
Start with Gauss’ Law and find the electric field due to a plane of
charge with surface charge density . In terms of 0, and .
14.
A spherically symmetrical but nonuniform volume distribution of
charge produces an electric field of magnitude E=Kr4, directed radially outward from the
center of the sphere. Here r is the radial distance from the center, and K is the constant.
What is the volume density  of the charge distribution?
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
15. A parallel plate capacitor is shown below (two oppositely charged planes) they are a
distance d apart and have an area of A
+
d
-
Answer the following in terms of A, and d.
a. Starting with Gauss’ law, find the electric field between the plates
b. Starting with Gauss’ law, find the electric field outside the plates.
16. An infinite charged non-conducting cylinder of charge density  and radius b is shown
below. Starting with Gauss’ Law find
a. The electric field at r>b
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
b. The electric field at r<b, that is inside the cylinder.
17. A spherical cloud of charge of radius
R contains a total charge +Q with a
nonuniform volume charge density
that varies according to the equation
where r is the distance from the center of
the cloud. Express all algebraic answers in
terms of Q, R, and fundamental constants
(a) Determine the following as a function of r
for r > R.
i. The magnitude E of the electric field
(b) A proton is placed at point P shown above and released. Describe its motion for a long time
after its release.
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
(d) Derive an expression for ρo
(e) Determine the magnitude E of the electric field as a function of r for r < R
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
18. In the figure above, a nonconducting solid sphere of radius a with charge +Q uniformly
distributed throughout its volume is concentric with a nonconducting spherical shell of inner
radius 2a and outer radius 3a that has a charge -Q
uniformly distributed throughout its volume. Express all
answers in terms of the given quantities and fundamental
constants.
(a) Using Gauss's law, derive expressions for the
magnitude of the electric field as a function of radius r
in the following regions.
i.
Within the solid sphere (r < a)
ii.
Between the solid sphere and the spherical shell (a < r < 2a)
2011 1st Take Home Assignment that Counts as a Test Grade of 2nd Trimester
iii.
Within the spherical shell (2a < r < 3a)
iv.
Outside the spherical shell ( r > 3a )