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1. (40 pts.) 4B SP12 REFERENCE: POTENTIAL OF A CHARGED CONDUCTOR:
QUIZ 3 #28.

Spherical Symmetry. A solid spherical conductor has uniform  negative total  charge Q < 0 (in coulombs) on the surface. The conductor has  radius B .  Check  the diagram below. Here's  some of the physics you should know about. (Use symbols always):

(a)    (5 points)  What is the  magnitude E of the electric field at point P at a
 distance  B/2 from the center ? Explain    your answer. 

(b)  (10 points) What is the magnitude E of the electric field at point P' at a distance
       B/2  from the surface of the conductor?  Derive E.  Show all steps. Look
       carefully at the diagram below before you begin the solution.

(c)  (5 points) What is the magnitude E of the electric field at point P'' 
       just above the surface of the  conductor ? Derive E.  Show all steps.
(d) (5 points)What is the direction of the electric field vector  at point
        P'  ?  Indicate by drawing an arrow at that point.

(e)  (3 points) What is the direction of the electric field vector  at point 
        P'' ?  Indicate by drawing an arrow at that point.

(f)   (6 points) What is the potential V at  point P’ at distance  B/2  from 
       the surface of the conductor?

(g)  (3 points) What is the potential V at point P''   just above the surface
       of the  conductor ?
(h)  (3 points) What is the potential V at point P at distance  B/2 from  the center ?

2. (26 pts.) 4B SP12 REFERENCE: POTENTIAL OF A CHARGED DISK:
, CONSERVATION OF ENERGY CH.23 #68 (NOT ASSIGNED) ;
QUIZ 3 #34 ; #9, #12, 14, 16;

Now check this out. A disk of radius R has an area charge density s > 0 in units  C/m² . For all solutions below, use symbols. Above the disk at a distance R from the center is a charge of mass m and charge q. The charge is released from rest, and moves upward to a  distance 2R from the center. Ignore gravity.
(a) (5 points) What is the sign of q,  positive or negative ? Circle one of the words.
 (b) (21 points) What is the speed of the point charge q when it reaches the
distance 2R ? Show  all steps. That means show all steps needed for the integration. Your final answers will be in symbols.


 
 

 

3. EXTRA CREDIT. 12 points.
A spherical  capacitor has charge Q on the inner  shell  and charge -Q on the  outer shell. The outer shell has radius b and the inner radius a. Check  the diagram below. It might be a highly simplified model of  a charged spherical gaseous layer surrounding a small planet. Here's  some of the physics you should know about this scheme. Use symbols always:

(a)  (2 points)  Find the  magnitude E of the electric field at a distance  r from the central axis of the capacitor if   r < a ?

(b)  (2 points)  Find the  magnitude E of the electric field at a distance  r   from the central axis of the capacitor if   r > b
(c)  (8 points) Derive the capacitance of the system.
(