PH 211 07-11-2014

Physics 211 Exam-1

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SIGNATURE and ID: ___________________________ Return this hard copy exam together with your other answer sheets. Write down your name on the back of the package of sheets you turn in.

Show all your procedures when giving the answer to the questions. Use additional sheets of paper if necessary

1. 1A The figure below shows 4 spheres of different radius, with charge uniformly distributed through its volume.

(5 points) Rank the spheres according to their volume charge density,, greatest first

a) I , II , III , IV b) I , II , IV, III c) III , IV, I, II

d) IV , III , II, I e) NA

(5 points) Rank the spheres according to the magnitude of the electric field they produce at P, greatest first

a) I = II , III = IV b) I = II , III, IV c) III=IV, I, II

d) IV , III , II, I e) NA

1B. There exist a non-uniform electric field E

(x, y, z) = 5 y j (with y in meters,

and E in N/C). The figure shows a Gaussian surface (a cube of side L= 4 m.)

X

Y

Z

L = 4 m

A

B C

D

E

F

(5 points) The total flux through the gaussian surface is (in units of N.m2/C):

a) 40 b) 320 c) 100 d) zero e) NA

(5 points) The total charge inside the gaussian surface is (in units of Coulomb): a) 1.87 x 10-12 b) 3.58 x 10-10 c) 0.12 x 10-9 d) 2.83 x 10-9 e) NA

1C (5 points) The figure (see next page) shows two point charges of charge +3q and

– q respectively located along long the x-axis and equidistance from the origin. Draw, approximately to scale, the electric field lines everywhere in the whole space around and beyond the location of the charges. In particular indicate the orientation of the electric field lines passing through the discrete points indicated in the figure (The dashed lines are shown just for reference).

(Use this graph to provide your answer to question 1C)

1D (5 points) The figures below show two separate cases, where all the different objects have positive charge uniformly distributed; Q > q and Q2 > q1. The figure on the left shows two solid spheres, of different radius, separated by a distance “d”. The figure on the right shows a small solid sphere in front of a thin bar of length “L”. Assuming that the charges are uniformly distributed all over the volume of the corresponding object, indicate which of the following statement(s) is (are) correct:

q Q

d

L

Q2

q1

a

a) The magnitude of the electrostatic force acting on the sphere of charge Q is

greater than the magnitude of the electrostatic force acting on the sphere of

charge q.

b) The magnitude of the electrostatic force acting on the sphere of charge Q is

lower than the magnitude of the electrostatic force acting on the sphere of

charge q.

c) The magnitude of the electrostatic force acting on the thin bar of charge Q2 is:

2

12

0

2

La

4

1

qQ

F

d) The magnitude of the electrostatic force acting on the sphere of charge q1 is:

2

12

0 a4

1 qQF

e) All the expressions above are incorrect.

1E (5 points) The four particles for a square of edge length a= 5 cm. The values of the charges are:

q1 = + 10 nC, Q2 = - 20 nC, Q3 = + 20 nC, q4 = - 10 nC

Draw the total electric field that exists at the center point of the square. (Just sketch the electric filed vector on the graph. No need to provide a

numerical value).

a

a q4

Q2

Q3

q1

answer

2. 2A (15 points) The figure at the right shows portions of two infinitely large,

parallel, non-conducting sheets, each with a fixed uniform charge. The

surface charge densities are 1 = 6 C/m2 and 2 = - 2 C/m

2. Calculate the

electric field at point “H” (located midway between the plates)

+

H

+

+

+

+

+

+

+

+

+

-

-

-

-

-

-

2B The figure below shows a small non-conducting ball of mass m = 10-3 Kg and

charge q= + 2 x 10-8C hanging from an insulating thread that makes an angle

=37o with a vertical plane sheet. The infinite non-conducting plane sheet is

uniformly charged (the figure shows its cross section). Assume that the sheet

extends far vertically, and into and out of the page.

Consider also that the gravitational force is acting on the ball.

a) (5 points) Draw the free-body-diagram for the ball.

b) (15 points) If the ball is in equilibrium, calculate the surface charge density

of the sheet:

3. The figure shows a bowl in the form of a ½ spherical shell of radius R=3 cm with its

center at the point P. A total charge of Q= 9 C is uniformly distributed over its

surface.

3A (10 points) Calculate the surface charge density.

3B (10 points) Calculate the electric potential V at point P.

3C (10 points) Calculate very explicitly the electric field vector E at point P.

Hint: Divide the bowl into rings of different radius, and add up the contribution to the fields from the different rings

Q

SIDE VIEW CROSS SECTION

VIEW q1

Z

P

All the charges on the bowl are equidistant (a distance R) from the point P.