THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 14:
 
POTENTIAL & CAPACITANCE
 
Thu. 01 Feb. 2001 - finish by Wed. 07 Feb.

1.

Hole in a Plane of Charge: A large flat non-conducting surface (treat it as an infinite sheet) carries a uniform charge density $\sigma = 4.0 \times 10^{-9}$ C/m². A small circular hole has been cut out of the middle of this sheet of charge, as shown on the diagram. Calculate the electric field at point P a distance z = 1.0 m up from the centre of the hole along its axis. The radius of the hole is R = 0.4 m.

2.

$\parbox{4.75in}{% {\Large\bf Triangle of Charges: } Derive an expre . . . . . . tre of the triangle. (Initially the charges are all infinitely far apart.) }$  

3.

$\parbox{4.25in}{% {\bf ARRAY of CAPACITORS: } The battery $B$\space . . . . . . the charge on each capacitor if $S_2$\space is also closed? \end{enumerate}}$  

4.

CAPACITOR WITH INSERT: Suppose we have a capacitor made of two large flat parallel plates of the same area A (and the same shape), separated by an air gap of width d. Its capacitance is C. Now we slip another planar conductor of width d/2 (and the same area and shape) between the plates so that it is centred halfway in between. What is the capacitance $C^\prime$ of the new system of three conductors, in terms of the capacitance C of the original pair and the other parameters given? (Neglect ``edge effects'' and any dielectric effect of air.)

0.4in

. . . and Tipler (4$^{\rm th}$ Edition)

Ch. 24: problems 19, 49, 65 and 97

Ch. 25: problems 33, 54, 57, 67, 101 and 109

Challenge Problems:

1.

THUNDERCLOUD CAPACITOR: A large thundercloud hovers over the city of Vancouver at a height of 2.0  km. Between the cloud and the ground (both of which we may treat as parallel conducting plates, neglecting edge effects) the electric field is about 200  V/m. The cloud has a horizontal area of 200  km².

(a)

Estimate the number of Coulombs [C] of positive charge in the cloud, assuming that the ground has the same surface density of negative charge.

(b)

Estimate the number of joules [J] of energy contained in the air between the cloud and the ground.

2.

CUBIC CAPACITOR: Suppose we take a roll of very thin ( 50  $\mu$m) copper sheet and a roll of 150  $\mu$m thick strontium titanate dielectric (dielectric constant 310) and form a capacitor as follows: cut the sheets into strips 5  cm wide and sandwich the dielectric sheet between two sheets of copper. Then fold the sandwich back and forth to fill a cube 5  cm on each side. Assuming that we can press the layers together firmly so that there are no empty spaces, find:

(a)

the capacitance of the resulting cube-shaped capacitor;

(b)

the total energy we can store in this small cube.