PHY101 Final Term Highlights by Math Liner

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, 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 q q q q F F k r r

ured in Coulombs (C) and with

8. 85 10 and hence 8.99 10
9. 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

ˆ rce of force. In vector form, is the force exerted by 2 on 1,

ˆ ˆ where the unit vector is . On the other hand, is the force exerted

by 1 on q q F r r

r q q r F r r r

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 F F

F F F F

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.

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) e e

(neutral pion annihilates into neutral photons)

(two deuterons turn into tritium and proton)

5. this a quantity that has a defin H H H p

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

uid, or even a sugarcane field. In Electrostatic is a combination of 2 words electro and statics elctro means electric charge and static means at rest. electrostatics, the study of electromagnetic phenomena that occur when there are no moving charges—i.e., after a static equilibrium has been established. Charges reach their equilibrium positions rapidly, because the electric force is extremely strong.

According to Coulomb's law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Yeh situation gravity jaisi hi hai, lekin yahan force mass ki wajah se nahi, electric charges ki wajah se hoti hai.

Yani jitni force 2 ne 1 par lagayi, utni hi 1 ne 2 par lagayi, lekin ulte direction mein.

Charge har kisam ke amount mein nahi hota, ye sirf choti choti fixed units mein hota hai jaise e, 2e, 3e, etc.

Charge na kabhi banaya ja sakta hai aur na khatam. Kisi bhi reaction ya event ke pehle aur baad total charge hamesha same rehta hai.

Field wo cheez hai jo space mein kisi bhi point par value batati hai.

Scalar field: sirf aik value hoti hai (jaise temperature) Vector field: direction aur value dono hoti hain (jaise hawa ka rukh ya electric field) every case, there are 3 numbers: ( , , , )

6. 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

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 . H F q E q 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 and so

. A way to visualiz q

qq F r

F q E q r 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.

7. Typical values for the maginitud e of the electric field

Inside an atom10 N/C

Inside TV tube10 N/C E

-2 In atmosphere10 N/C

Inside a wire10 N/C

8. 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 can then be found from mg q q E

9. 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

q E E k r 2 ˆ ˆ 1,2,3, . Here is the unit vector pointing from the charge to

the point of observation. i i i r i r E eE

mg y McQs Yani agar kisi charge se doosri jagah par kisi test charge par force lagti hai, to woh electric field kehlata hai.

Lines positive charge sy niklti hain or Negative charge par khatam hoti hain

Agar ek charged particle par gravity ka force aur electric field ka force barabar ho jaaye, to hum charge *q* nikal sakte ha

Agar bohot se charges hon, to har charge ki electric field alag alag calculate kar ke sab ko add kr do

10. Let us apply the principle we have just learned to a system of two charges and -

which are separated by a distance (see diagram). Then, . Just to make

things easier (not q q

d E E E

necessary; one can do it for any point) I have taken a point that lies

on the x-axis. The magnitudes of the electric field due to the two charges are equal;

. The

/ 2 q q E E r x d vertical components cancel out, and the net

electric field is directed downwards with magnitude, cos cos cos .

/ 2 From the diagram below you can see that cos . Substituting

/ 2 E E E E

d

x d this, we

/ 2 find:

/ 2 / 2 / 2 q d qd E

x d x d x d

11. The result above is so important that we need to discuss it further. In particular, what

happens if we are very far away from the dipole, meaning ? Let us first define

the x d

dipole as the product of the charge the separation between them

Then, . In the above,

/ 2

/ 2 has been neglected in moment p qd

p p d p E x x x x d x

d x comparison to 1. So finally, we have found that for

12. It is easy to find the torque experienced by an electric dipole that is placed in a uniform

electric field: The magni x d

p E x

tude is sin sin sin , and the direction is

perpendicular and into the plane. Here is the angle between the dipole and the electric

field. So sin sin . d d F F Fd

qE d pE

r · r · d

x

E

E E Agar do barabar magnitude wale charges (ek positive aur ek negative) d faaslay par hon, to unki electric fields opposite directions mein hoti hain. Horizontal components add hote hain Vertical components cancel ho jaate hain Final electric field downward hoti hai.

Dipole moment = charge × distance between charges

Agar point bohot door ho (x >> d), to field simplify ho jaati hai