Capacitors: Electric Charge

2010 회로 및 전자기학 숙제 #2
제출 2010년 3월 19일 (금) C319
1. Three point charges Q1  9 C , Q2  4 C , Q3  36 C are arranged on a straight line. The distance between Q1 and Q3 is 9cm. It is claimed that a location can be selected for Q2 such that each charge will experience a zero force. Find this location. 2. A line charge of uniform charge density

l

forms a circle of radius b that lies in the

xy-plane in air with its center at the origin.



a) Find the electric field intensity E at the point (0, 0, h).



b) At what value of h will E in part (a) be a maximum? What is this maximum?

3. Determine the work done in carrying a

 5 C charge from P1 ( 1, 2,  4) to

 

P2 (2, 8,  4) in the field E  a x y  a y x
a) along the parabola y  2x , and
2

b) along the straight line joining P and P2 .
1

4. A finite line charge of length L carrying uniform line charge density

l

is coincident

with x-axis.
a) Determine V in the plane bisecting the line charge.



b) Determine E from

l

directly by applying Coulomb’s law.

5. The polarization in a dielectric cube of side L centered at the origin is given by





P  P0 (a x x  a y y  a z z ) .
a) Determine the surface and volume bound-charge densities.
b) Show that the total bound charge is zero.

6. The space between a parallel-plate capacitor of area S is filled with a dielectric whose permittivity varies linearly from

1

at one plate (y=0) to

2

at the other plate

(y=d). Neglecting fringing effect, find the capacitance.

7. Three capacitors

1 C , 2 C , and 3 C are connected as shown in Figure across a

240-volt source. Calculate the electric energy stored in each capacitor.

1F
2 F
3F

+

-

240(V)

8. A parallel-plate capacitor of width w, length L, and separation d has a solid dielectric slab of permittivity



in the space between the plates. The capacitor is charged to a

voltage V0 by a