PHYS2012
MID SEMESTER TEST 2010
ELECTROMAGNETIC PROPERTIES OF MATERIALS
Question 1 (10 marks)
Consider a daily journey to and from work, a distance of 60 km in an electric car.
Assume the energy required for the journey is U = 4.60×107 J. The electric car is
powered by banks of ultracapacitors. The capacitance of each capacitor is Cu = 3000 F
and the maximum voltage across each capacitor is Vu = 2.00 V. The voltage across the
capacitor bank is V = 100 V.
(a)
Draw a diagram of how the capacitors can be arranged in a series / parallel
combination to provide the energy for the journey.
(b)
What is the total charge Q that must be stored by the capacitor bank to provide the
energy for the journey?
(c)
What is the equivalent capacitance of the capacitor bank C?
(d)
How much energy is stored by each individual capacitor Uu?
(e)
What is the number of individual ultracapacitors N needed to store the energy
required for the journey?
Question 2 (10 marks)
The parallel plate capacitor shown has a plate area A and separation distance d and has a
charge of Q. The free charge surface density is f = Q/A. The space between the slabs is
filled by two dielectric slabs are equal thickness (d/2) but difference dielectric constants
(  r1 and  r 2 ).
Slab 1
Slab 2
 r1
d/2
r2
d/2
Show and justify the following:
(a)
Electric displacement D   f 
(b)
Electric field E1 
(c)
(d)
(e)
(f)
f
 r1  0
E2 
Q
A
f
r2 0
  1 
  1 
Polarization P1   f  r1  P2   f  r 2 
  r1 
 r2 
 Q d   r1   r 2 
Potential difference between the plates V  


 2  0 A    r1  r 2 
 2 A     
Capacitance C   0   r1 r 2 
 d   r1   r 2 
Net bound charge surface density at the interface between the two dielectric slabs
  
 bnet   f   r1   r 2 
  r1  r 2 