THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 5:
 
ELECTRIC  POTENTIAL  &  CAPACITANCE
 
2 Feb. 2000 - finish by 9 Feb. 2000

Tipler Ch. 20, problems 43, 45, 51 & 63;

1.
Triangle of Charges: Derive an expression for the work required to bring four charges together into an equilateral triangle of side a (as shown) with one charge at the centre of the triangle. (Initially the charges are all infinitely far apart.)


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2.
Hole in a Plane of Charge: A large flat non-conducting surface 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. Ignoring ``fringing'' of the field lines around all edges, 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.


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3.
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 maximum charge it will hold without breaking down;
(c)
the total energy we can store in this small cube.

4.
ARRAY of CAPACITORS: The battery B supplies 6 V. The capacitances are C1 = 2.0 $\mu$F, C2 = 1.0 $\mu$F, C3 = 4.0 $\mu$F and C4 = 3.0 $\mu$F.
 
(a) Find the charge on each capacitor when switch S1 is closed but switch S2 is still open.
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(b) What is the charge on each capacitor if S2 is also closed?

5.
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.

. . . and Tipler Ch. 21, problems 29, 35, 39, 55 & 61.


Jess H. Brewer
2000-02-02