SP ’11, TEST 1

1.  (35 points)   A charge of magnitude  q  = 4.00x10 -3 C is placed at each corner of a square with side a = 0.100 m.  The charges at the upper left and lower  right corners are negative.  The charges at the upper right and lower left corners are positive.


What is the

(a) (20 points) magnitude

and

 (b) (15 points)  direction

 

of the net force on the charge at the lower right corner ?

Show all work on this and the next two blank pages.  For maximum partial credit , derive your answers using a, q and other
symbols until you plug in numbers at the last step. However, do the problem with any method as long as you  show your work.  Be careful if  you plug in numbers earlier in the process .

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2.  (35 points)  In this  problem ignore the force of gravity.   An electron is in the region of a uniform electric field directed along the vertical. Starting from
rest, if the electron  moves vertically upward  on the page and speeds up to 50% the speed of light over a vertical distance of  2.00 cm,

(a) (15 points) what is the direction  and

(b) (20  points)  what is the magnitude E

of the electric  field?

In both parts (a) and (b),  show and explain all work leading to your answer.

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3. (35 points ) An electron starts from rest 30.00 cm away from a fixed point charge with Q = +0.100 µC .

How fast will the electron be moving when it is 15.00 cm away from the fixed charge?
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4.  (11 points)  Below,  a rectangular solid is made of carbon with sides 2.00 cm, 8.00 cm and 4.00 cm  lying on the x, y and x axes in that order. The resistivity is ρ = 3.10x10-5 ohm-m.  Current is allowed to pass in the x direction,  y-direction or  z-direction only.  For each possible current direction, you connect wires from a battery  across the two opposite faces perpendicular  to the current.

Determine the resistance R for  current that passes along the 

(a) (3 points) x direction,

(b) (3 points) y direction,

(c) (3 points) z direction.

For the next two parts, assume for  each possible current direction, the same voltage difference V is placed across the two opposite faces perpendicular  to that current.

(d) (1 points) Which current is the largest,   current in x-direction, current in y-direction or current in z-direction? Explain.
(e) (1 points) Which current is the smallest ,  current in x-direction, current in y-direction or current in z-direction? Explain.

 

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5.  (35 points) A special extension cord  has length L = 5.00 m  and rectangular  cross-section given by width w =  0.100 cm and small length  = 0.070 cm . Between the ends of the cord there is a voltage difference given by V+  -  V-   . The current I = 12.0 (A) . See diagram below .

(a) (20  points)   What is the voltage difference V+  -  V-   ?

(b) (10   points)  What is the rate of heat generation (in Watts)  in the cord?
(c) (5 points)   How much heat is generated (in Joules) in a time period of 5 minutes? 
(d) (7 points) EXTRA CREDIT.  What is the magnitude E of the electric field in the  extension cord?