Download tutorial 2: answer

EKT 241: ELECTROMAGNETIC THEORY
SEM 2 2010/2011
ANSWER FOR TUTORIAL 2: ELECTROSTATICS
1. Calculate the total charge on a circular disk defined by r  a and z  0 if:
a)
 s   s 0 e  r (C/m 2 )
b)  s   s 0 sin  (C/m )
2
where  s 0 is a constant. The unit of r is in meter.
2. Electric charge is distributed along an arc located in the x-y plane and defined by r = 2cm and
0     / 4 . If  l  5C / m , compute E at (0,0, z ) and then evaluate it at:
a) The origin.
b) z = 5 cm
c) z = -5cm
3. The electric flux density inside a dielectric sphere of radius a centered at the origin is given
by:
ˆ  R (C/m 2 )
DR
0
Where  0 is a constant. Calculate the total charge inside the sphere.
4. In a certain region of space, the charge density is given in cylindrical coordinates by the
function:
V  20re  r (C/m 3 )
Apply Gauss’ Law to compute D.
Solution: Draw Gaussian surface:
5. Three point charges, each with charge value q  3n C , are located at the corners of a triangle in
the x-y plane, with one corner at the origin, another at coordinate (2cm, 0, 0) and the third corner
at coordinate (0,2cm, 0) . Calculate the force acting on the charge located at the origin.
6. In a dielectric medium with  r  4 , the electric field is given by
E  xˆ ( x 2  2 z )  yˆ x 2  zˆ ( y  z ) (V/m).
Calculate the electrostatic potential energy in the region  1m  x  1m , 0  y  2m and
0  z  3m .
7. With reference to Figure 1, find E1 if E2  xˆ 3  yˆ 2  zˆ 4 (V/m) ,  1  2 0 ,  2  18 0 and the
boundary has a surface charge density  s  7.08  10 11 (C/m 2 ) .
Figure 1