Coulomb's law describes the electrostatic force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The law leads to the concept of electric field as a vector field that describes the electromagnetic force exerted on charged objects. Electric field lines are a graphical representation of the electric field, with properties like direction, strength, and superposition. Coulomb's law and electric fields can be applied to understand phenomena like dipoles, parallel plates in a capacitor, and spherically symmetric charge distributions.

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 =kq1q2 /r2

3. b) Units
Two possibilities:
- define k and derive q (esu)
- define q and derive k (SI) √
9 ×109
N =k(1C)2
/(1m)2
⇒k =9 ×109
N

4. • For practical reasons, the coulomb is defined using current and
magnetism giving
k = 8.988 x 109
Nm2
/C2
• Permittivity of free space
2212
0 Nm/C1084.8
4
1 −
×==
kπ
ε
Then
F =
1
4πε0
q1q2
r2
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
q1
q2
q3
q
F3
F2
F1
Net force on q: F = F1 + F2 + F3
F

6. Electric Field
- abstraction
- separates cause and effect in Coulomb’s law
a) Definition
r
E =
r
F
q0
Units: N/C

7. b) Field due to a point charge
F
Q
q0
r
Coulomb’s law: F =k
Qq0
r2
Electric Field: E =F /q0 = k
Q
r2
r
E //
r
F ⇒direction is radial

8. c) Superposition of electric fields
Net field is the vector sum of fields from each charge
P
E3
E2
E1
Net field at P: E = E1 + E2 + E3
E
q1
q2
q3

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
4πr2 ∝
1
r2
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, σ=q/A
02ε
σ
=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-
ER=0
E+
E-
EL=0
• Strong uniform field between: E =σ/ε0
• Field zero outside

17. f) Spherically symmetric charge distribution
+ +
+
+
++
+
+
• Symmetry ==> radial
• number of lines prop. to charge
Outside the sphere:
r
E =
kq
r2
ˆr
as though all charge concentrated at the
centre (like gravity)