It is electrostatics notes from class 12 physics book, Study notes of Physics

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Chapter

Electrostatic Potential Notes

Electric Potential^ Difference :-(

or)

It is defined as the amount^ of workdone^ in

moving

a unit^ positive charge from^

one point

to another^ against

Electrostatic force without

any acceleration " > (^) E i. DV^ = ¥ Ago >

• • > 2 1 V V or (^) V2 >
• V =W÷ > Electric Potential :-(

V)

" The amount (^) of workdone^ in^ moving a unit positive (^) charge from^ infinity^ to^ the^ reference

point against the^

electrostatic force without any acceleration (^). " ☐ v=wq÷ > (^) c- or =⑨• V2 -^ Vi =w÷ =-3Has^ - V2-^ un = wqe;- > . '

. Van^ = (^0) V

Weg or ✓^ = (^) We 90

Wen KQ^ qodr^ cos^0 ( p →a) =fp÷, Weucp →^ a) = fp°÷Qqodr cos^180 " = - fi k9÷dr = - Kato fp° ᵈ ÷ = - Kaan 1- ÷]^? Here (^) , Per = - Kaa. /

• ÷ ] (^)? = - Karol .

÷

t :-)) = - kdao ( ÷) were = (P^ - >a)^ _kQ÷ 08 Were = tkQ÷

② (^00 →^ P)

Put eq② in^ eq①

ax = ";%= /"=¥=/

or

H

Principle of^ superposition for^ Electric Potential " EP at^ a (^) point due^ to^ system of^9 92 charges

can be^ calculated^ by^ finding

the (^) algebric sum (^) of E.P.^ due^ to 9 6 97 individual (^) charges "

. - - an V (^) net =^ Vi^ 1-V2^ 1-^ V3^ t^ -^ -^ 1- Vn

ii ) At Equitorial Position!^

• p ✓^ =^? By

Py

. theorem?^ - ÷ ' , ' v2 = x2 +^ r ! ; i^ r in ' ' , I " (^) ' or= (^) Ntt

• q +^ q we (^) have to calculate (^) the E. P. (^) at

point

'P! ✓net =^ ✓^ itV^

• ① For charge oh (^) , For charge qz ✓ 2=+1%4%- " =

• ② Put (^) 2,3 in^ eq① ✓ (^) net = _¥g+ :-# = °

E.^ P^.^ at^

any point^ : - axial post ◦ ¥ 0 .ie#PCosOa:¥ 0 ¥ 10 →^ p^ _ or iii. ÷ : Equatorial ! 9 k →p '

-. Psino Consider (^) an E.D. , let ☒^ be the

arbitary point^

, when^ E.^ P^.^ is^ to^ since calculated.

✓ net =^ ✓^ axial^ 1-^ Veg.

We know^ that^ :^

✓axial = K÷cosO Veg

_- 0 Gino)

✓ = Kat cost to^ (^ Sino) ✓ = K÷cosO ✓ = Pj COSO

(^) EQUIPOTENTIAL SURFACE

It is an imaginary surface^

on which^ Electric

potential

is same ( constant)^ only 3D^ surface^

.

ii ] No work is (^) done by (^) moving a charge on equipotential

surface

Av=w÷ .

• A (V) % Eqn Surface : -^ DX -^ -^ O^ Wen^ :O 0 = 1 ¥ > (^) • Bev,

lWex

Iii (^) ) The^ direction^ of^ Electric (^) field is^ always perpendicular to Equipotential surface . iv ) No^ Equipotential

Surface

can intersect^ each other.

We thus arrive at two important conclusions concerning the relation between electric field and potential which are as given below : i) Electric field is in the direction in which the potential decreases steepest. ii) Its magnitude is given by the change in the magnitude of potential per unit displacement normal to the equipotential surface at the point.

Relation^ between Electric (^) field and (^) Potential : -

i) when (^) E. f. is (^) uniform : - s AV=Wqe ˢ

• ① q % tax workdone^ :^
• i ÷ , were =^ t.eu.^ do^ > . :^ ten =^ - q C- Were =^ - qedr ii^ )^ E.^ f.^ is (^) Non

Uniform

? - Put (^) ② in^ ①^ r2 were All = f Edr (^) ☒Y ov= -9yd "

1wv=-E

Potential^

Gradient :^

" Rate (^) of change in^ Potential with^ respect to^ distance^ " EPD :^ - y

• • • • +^ + + ++

d Fen

↑ . All =^ WI -^ ①^ I^ a. ↓ (^90) Fei work done^ :^

• • • (^) - - - - - (^) - - Wen =^ - ten ✗^ d-②

Electric Potential^ Energy

( U^ ) :^ -

changing in (^) the potential (^) energy of^ the

system

is

equal

to the^

negative

of workdone^ by Electric force of^ the

system

" +Wet du =^ -^ Wet^ V2-^ U, =^

• (^) Wee ⑨ → ← du =^ +^ Wen^ uz-^ V1 =^ +^ Wen^ -^ Wen KE =^ Wee^ +^ Were kE Electric Potential^ Energy for^ 2 Charged Particle: - #①⑨ ④g-

• (^) 4- -^ - dr (^) •

Let us^ assume^ that^ point charges qilqz are

kept at a (^) fixed location^ as shown^ in^ fig . We have^ to^ calculate^ E. P. (^) E.^ : - du =^ -^ W^ total V2 - Ui =^ -

[

Witwz] - ① Workdone^ in^ bringing charge q ,^ from oo^ :^

W (^) , so^ &^ V1^ =D^ - ② Workdone (^) in

bringing charge^ qz^

from D:^

Wai (^) f! Fdr was fair (^) k%÷ndr

• ③

Put ②③^ in^ ①^ :^

uz -^ ◦^ =^

[ ◦ + fair k% ˢ dr ] V2 =^ -1< for ¥ 2 dr Uzi -1< [

÷]^? V2 = -1<

÷

• ( - to (^) )) 02 = -1<91, or U^

÷.^ %÷ Electric Potential^ Energy of^ E. D. (^) in Uniform EF :

> > ⊕ ¢ 2 ⊕ > > l (^) e

• --- -^ -1- ' (^) I > .

l Tl

1 > ⊖ (^) s (^) > > ⊖

consider a^ dipole

with charge tq^ & - q placed

in uniform E.^ f.^ As^

we know that^

in uniform

E. f.^ dipole experiences : -^ Net^ Torque (Force]

|u=-PECo✓

or

1U=_p

Case I) 0=900,

. T=PESinO U=

• (^) PECOSO

T-PEma×

min case -1-1^ ) 0=00^ , 180° T=PEsinO (^) U = -^ PECOS^ 0°^ U=^ -^ PECOS^180

Pinin FPE^

"

1U=+p

min (^) Max

[

Zakisaudagar

Zaki_^ Sir

• (^) -

Zakka≥ -