Post on 17-Jan-2017
transcript
Coulomb’s Law and its applications
Prepared by:Sweetu Ratnani (130010111048)
Guided by:Shailesh Khant (EC. Dept)
Coulomb’s Law
a) form
F kq1q2 /r2
b) Units
Two possibilities:- define k and derive q (esu)- define q and derive k (SI) √
9 109N k(1C)2 /(1m)2
k 9 109N
• For practical reasons, the coulomb is defined using current and magnetism giving
k = 8.988 x 109 Nm2/C2
• Permittivity of free space2212
0 Nm/C1084.841 k
Then
F 1
40
q1q2
r2
c) Fundamental unit of chargee = 1.602 x 10-19 C
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
Electric Field
- abstraction- separates cause and effect in Coulomb’s law
a) Definition
r E
r F q0
Units: N/C
b) Field due to a point charge
F
Q
q0
r
Coulomb’s law:
F kQq0
r2
Electric Field:
E F /q0
kQr2
r E //
r F direction is radial
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
Electric Field Lines (lines of force)
a) Direction of force on positive charge
radial for point chargesout for positive (begin)in for negative (end)
b) Number of lines proportional to charge
Q2Q
d) Line density proportional to field strength
Line density at radius r:
Number of linesarea of sphere
N
4r2
1r2
Lines of force model <==> inverse-square law
Applications of lines-of-force model
a) dipole
b) two positive charges
c) Unequal charges
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, =q/A
02
EBy comparison with the field from a point charge, we find:
E
q, A
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 /0
• Field zero outside
f) Spherically symmetric charge distribution
+ +
+
+
++
+
+
• Symmetry ==> radial• number of lines prop. to charge
Outside the sphere:
r E
kqr2 ˆ r
as though all charge concentrated at the centre (like gravity)