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Electrostatics I-Classical Physics-Handouts, Lecture notes of Classical Physics

University of AllahabadClassical Physics

This course includes alternating current, collisions, electric potential energy, electromagnetic induction and waves, momentum, electrostatics, gravity, kinematic, light, oscillation and wave motion. Physics of fluids, sun, materials, sound, thermal, atom are also included. This lecture includes: Electrostatics, Charge, Coulumb, Law, Newton, Equality, Proprtionality, Quantized, Vector, Proton, Conserved, Scalar, Field

Typology: Lecture notes

2011/2012

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PHYSICS –PHY101 VU
© Copyright Virtual University of Pakistan
61
Summary of Lecture 22 – ELECTROSTATICS I
1. Like charges repel, unlike charges attract. But by how much? Coulomb's Law says that
this depends both upon the strength of the two charges and the distance between them.
In mathematical ter 12 12
2 2
ms, which can be converted into an equality, .
The constant of proportionality will take different values depending upon the units we
choose. In the MKS system, charge is meas
qq qq
FFk
rr
∝=
0
12 2 2 9 2 2
0
1
ured in Coulombs (C) and with
4
8.85 10 / and hence 8.99 10 / .
2. The situation is quite similar to that of gravity, except that electric charges and not masses
are the sou
k
CNm k NmC
πε
ε
−
=
=× =×
12
12 12
2
012
12 1 2
12 21 21
2
12 0 12
1ˆ
rce of force. In vector form, is the force exerted by 2 on 1,
4
1
ˆˆ
where the unit vector is . On the other hand, is the force exerted
4
by 1 on
qq
Fr
r
rqq
rFr
rr
πε
πε
=
==
G
GG
12 21
1121314
2. By Newton's Third Law, . For many charges, the force on charge 1 is
given by,
3. Charge is quantized. This means that charge comes in certain units only. So th
FF
FF F F
=−
= + + +⋅⋅⋅⋅
GG
GG G G
19
e size of a
charge can only be 0, , 2 , 3 , where 1.602 10 is the value of the
charge present on a proton. By definition we call the charge on a proton positive. This
makes the c
eee e C
−
± ± ± ⋅⋅⋅⋅ = ×
harge on an electron negative.
4. Charge is conserved. This means that charge is never created or destroyed. Equivalently,
in any possible situation, the total charge at an earlier time is equal to the charge at a
later time. For example, in any of the reactions below the initial charge = final charge:
(electron and positron annihilate into neutral photons)
ee
γγ
−+
+→+
0
22 3
(neutral pion annihilates into neutral photons)
(two deuterons turn into tritium and proton)
5. this a quantity that has a defin
HH Hp
πγγ
→+
+→+
Field : ite value at any point in space and at any time. The
simplest example is that of a scalar field, which is a for any value of , , , .
Examples: temperature inside a room ( , ,
single number x y z t
Txyz
, ) , density in a blowing wind ( , , , ),
There are also which comprise of three numbers at each value of , , , .
Examples: the velocity of wind, the pressure inside a fl
txyzt
vector fields, x y z t
ρ
⋅
⋅⋅
uid, or even a sugarcane field. In
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Summary of Lecture 22 – ELECTROSTATICS I

  1. Like charges repel, unlike charges attract. But by how much? Coulomb's Law says that this depends both upon the strength of the two charges and the distance between them. In mathematical ter ms, 1 2 2 which can be converted into an equality, 1 22. The constant of proportionality will take different values depending upon the units we choose. In the MKS system, charge is meas

F q q^ F kq q r r

0 0 12 2 2 9 2 2

ured in Coulombs (C) and 1 with 4 8.85 10 / and hence 8.99 10 /.

  1. The situation is quite similar to that of gravity, except that electric charges and not masses are the sou

k

C Nm k Nm C

πε ε −

= × = ×

12 1 22 12 0 12 12 12 21 1 22 21 12 0 12

rce of force. In vector form, 1 ˆ is the force exerted by 2 on 1, 4 where the unit vector is ˆ^. On the other hand, 1 ˆ is the force exerted 4 by 1 on

F q q r r r r^ F q q r r r

πε

πε

G

G G

12 21 1 12 13 14

  1. By Newton's Third Law,. For many charges, the force on charge 1 is given by,
  2. Charge is quantized. This means that charge comes in certain units only. So th

F F

F F F F

G G

G G G G

19

e size of a charge can only be 0, , 2 , 3 , where 1.602 10 is the value of the charge present on a proton. By definition we call the charge on a proton positive. This makes the c

± e ± e ± e ⋅ ⋅ ⋅ ⋅ e = × − C

harge on an electron negative.

  1. Charge is conserved. This means that charge is never created or destroyed. Equivalently, in any possible situation, the total charge at an earlier time is equal to the charge at a later time. For example, in any of the reactions below the initial charge = final charge: e −^ + e +→ γ +γ (electron and positron annihilate into neutral photons) 0 2 2 3

(neutral pion annihilates into neutral photons) (two deuterons turn into tritium and proton)

  1. this a quantity that has a defin

H H H p

π → γ +γ

  • → +

Field : ite value at any point in space and at any time. The simplest example is that of a scalar field, which is a for any value of , , ,. Examples: temperature inside a room ( , ,

single number x y z t T x y z , ) , density in a blowing wind ( , , , ), There are also which comprise of three numbers at each value of , , ,. Examples: the velocity of wind, the pressure inside a fl

t x y z t vector fields, x y z t

ρ ⋅ ⋅ ⋅

uid, or even a sugarcane field. In docsity.com

every case, there are 3 numbers: ( , , , ) { 1 ( , , , ), 2 ( , , , ), 3 ( , , , ) }.

  1. The electric field is also an example of a vector field, and will be the most important for our purpose.

V x y z t = V x y z t V x y z t V x y z t

G

0 0

It is defined as the force on a unit charge. Or, since we don't want the charge to disturb the field it is placed in, we should properly define it as the force on a "test" charge q , E F. H q

20 0 2 0 0

ere is very very small. The electric field due to a point charge can

be calculated by considering two charges. The force between them is 1 and so 4 (^1). A way to visualiz 4

q

F qq r E F^ q q r

πε

πε

= = e E fields is to think of lines starting on positive charges

and ending on negative charges. The number of lines leaving/entering gives the amount of charge.

  1. Typical values for the maginitud (^11) 5

e of the electric field : Inside an atom- 10 N/C Inside TV tube- 10 N/C

E

2 In atmosphere-Inside a wire- 1010 -2 N/CN/C

  1. Measuring charge. One way to do this is to balance the gravitational force pulling a charged particle with mass m with the force exerted on it by a known electric field (see below). For equilibrium, the two forces must be equal and so. The unknown

mg = qE charge q can then be found from q mg. E

1 2 3

  1. Given several charges, one can find the total electric field at any point as the sum of the

fields produced by the charges at that point individually, or

i^ i i (^) i

E E E E

E E k q r

= (^) ∑ =

G G G G

G G

2 ˆ^ (^ 1, 2,3,^ ). Here^ ˆis the unit vector pointing from the charge to the point of observation.

∑ i r i i^ =^ ⋅ ⋅ ⋅ ri

E G

eE

G

mg^ G

y

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