Islamic Banking and Finance

1/27/2011

Electrostatics

Coulomb’s law – force between electrostatic charges 1. The electrostatic field 2. Electrostatics in free space 3. Coulomb’s law 4. The electrical field due to discrete distribution of charges 5. The electrical field due to a continuous distribution of charges

Charges
+ + Point charge + ++ -- + Surface charge Charge density– • Point • line l n (C/m) • surface s (C/m2) • volume v (C/m3) The total charge (Q) within a line/surface/volume studied is the integral of the charge density within the line/surface/volume. Q    l dl C
l

++--+---Line charge ++ ++ --

Volume charge

Q    s ds C
s

Q    v dv C
v

1

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Example of calculations
Determine the total charge within a sphere, of radius a, if the charge density within the sphere is v=kr. From the spherical coordinate system, dv=r2 sin dr d d And the total charge, Q, for the volume:

Q    v dv C
v

Therefore

Q

2

 0  0 r 0
2

 




a

 v r 2 sin drdd

 

 0  0 r 0

 

a

kr 3 sin drdd

2 4  ka  cos  0 4

 ka4

Elektrostatics in free space
Electric field intensity:
E lim F q0  0 q0

Is the force per unit charge if a very small static charge is placed in an electric field. F=qE In free space, divergence and curl of an electric field can be written as:

Divergence Differential form E=/0 Integral form E=0

Curl

 E  ds  
S

Q
0

 E  dl  0
C

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The electric field from a charged point
ar Q

A positively charged point, +Q, produces a spherical electric field. The electric field intensity from the charged point, at a distance R From the charged point can be written as:

 E  ds  
S

Q
0

ER  ds  ER 4R 2 
S





q

0

E  aR ER  aR

q 4 0 R 2

The positively charged point produes an electric field which has a direction flowing outwards from the point, and has a magnitude which is...