THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 3:
 
CAPACITANCE
 
25 Jan. 1999 - finish by 1 Feb. 1999

1.

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 $\kappa = 310$, dielectric strength 8 kV/mm) 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.

2.

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.

(b) What is the charge on each capacitor if S₂ is also closed?

3.

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.