Coulomb's law and its applications

coulombs law and its applications

1. Coulomb’s Law and its
applications
Prepared by:
Sweetu Ratnani (130010111048)
Guided by:
Shailesh Khant (EC. Dept)

2. Coulomb’s Law
a)form
 
F=kq
1q
2/r
2

3. b) Units
Two possibilities:
- define k and derive q (esu)
- define q and derive k (SI) √
 
9´10
9
N=k(1C)
2
/(1m)
2
 
Þk=9´10
9
N

4. •For practical reasons, the coulomb is defined using current and
magnetism giving
k = 8.988 x 10
9
Nm
2
/C
2
•Permittivity of free space
2212
0
Nm/C1084.8
4
1
-
´==
kp
e
Then
 
F=
1
4pe
0
q
1q
2
r
2
c) Fundamental unit of charge
e = 1.602 x 10
-19
C

5. d) Superposition of electric forces
Net force is the vector sum of forces from each
charge
q
1
q
2
q
3
q
F
3
F
2
F
1
Net force on q: F = F
1
+ F
2
+ F
3
F

6. Electric Field
- abstraction
- separates cause and effect in Coulomb’s law
a) Definition

 
r
E =
r
F
q
0
Units: N/C

7. b) Field due to a point charge
F
Q
q
0
r
Coulomb’s law:
 
F=k
Qq
0
r
2
Electric Field:
 
E=F/q
0
 
=k
Q
r
2

 
r
E //
r
F Þdirection is radial

8. c) Superposition of electric fields
Net field is the vector sum of fields from each charge
P
E
3
E
2
E
1
Net field at P: E = E
1
+ E
2
+ E
3
E
q
1
q
2
q
3

9. Electric Field Lines (lines of force)
a) Direction of force on positive charge
radial for point charges
out for positive (begin)
in for negative (end)

10. b) Number of lines proportional to charge
Q
2Q

11. d) Line density proportional to field strength
Line density at radius r:
 
Number of lines
area of sphere
 
=
N
4pr
2
 
µ
1
r
2
Lines of force model <==> inverse-square law

12. Applications of lines-of-force model
a) dipole

13. b) two positive charges

14. c) Unequal charges

15. d) Infinite plane of charge
+
+
+
+
+
+
+
+
+
+
+
+
Field is uniform and constant to ,
∞
in both directions
Electric field is proportional to the line
density, and therefore to the charge
density, s=q/A
02e
s
=E
By comparison with the
field from a point charge,
we find:
E
q, A

16. e) Parallel plate capacitor (assume separation small compared to the size)
+
+
+
+
+
+
-
-
-
-
-
-
E
+
E
-
E=2E
+
E
+
E
-
E
R
=0
E
+
E
-
E
L
=0
• Strong uniform field between:
 
E=s/e
0
• Field zero outside

17. f) Spherically symmetric charge distribution
++
+
+
++
+
+
• Symmetry ==> radial
• number of lines prop. to charge
Outside the sphere:

 
r
E =
kq
r
2
ˆ r
as though all charge concentrated at the
centre (like gravity)