Formula Cheat Sh eet Class 12 Physics

Electric

I
charges & Fields
Potential due to
Coulomb's Law E =

qa
1
r F =

er uniformly charged Sphere Non

Conducting Sphere
Outside
STE
9/43
a
9/4ItEor -x
=

⑪ N x =
-
* r> R
for vacuum for medium
on the shell 1-
E
V= V =

Electri field Electric field due to point

Intensity charge
I
r =
R 4ITEoR
.

/3 Y
⑪I ⑪
y=
*
9 r
90 ⑭ E inside y =

p
e I X
4,
k 1 ER UCR 41520 2R3
=F 9 source
=

charge E
=

R
4, 30
=

To stored in force between plates of

90= test
charge *
Energy a
Capacitor Capacitor
p
C
e
F Q Common Potential
W= QV=
a
=

Gauss's
=

#
Electric flux # Law
2 A So

Ataz= AltCae
y=
for uniform electric field ①= GE dE= Gin Net
charge enclosed Energy losS
=

Energy density
.

6 E E EACOSO
mone by the closed surface
24Cz(y
xz)
= =

SE
.

u 0
-
.

,
=
=

for non-uniform # Dipole (P) Y (C ,

# (2)
q I 9 p 1 = 9/2
/E
- +

I d
=

current
⑭ D

Electricity
= . ⑪
# 2a - Current density

U
---
a
=lectric current I
= #
&

for surface instantaneous

=

a closed
dipole placed
·
# in U E F
d
. .

caverage) i current I

E
=

& GE d Torque I IXE

= =
.

↓
force
#Electric field due to dipole Net
Resistivity
=0
Drift Velocity Mobility Ohm's law
Work done in rotation of dipole
At axial point
~ an
eET eXt M /d) m iR R
PA
=

Ya Y
= = =
= =

- from 0 00 U=PECCOSO , -10s02) E net

23
E .
mL
=

M
-E Electrostatic potential energy
5.
Relation blu iC Ye Relation blu J & F EMF of a cell
~ On the equitorial line U =
-

+E
-
J
IE
1
E=
=

RIS =Anee
E
charge density
=

E linear surface volume

Electric
-
power Energy E 1/ F In
q q E
=

x
~At
any general point
=
=
r =

1 =net iR
2
r
#Terminal Potential diff
=

E =

K !
BOS - A
P Vi
= =
=
V W =

vq
=
Vit
infinite M E
# EoF due to
Charge iRt Y
I
E- ir
13 E
=
r n = V =

20
=
=

sheet of
Due to
charged Conducting Sphere #Principle of Wheat stone
R

R/E)
EF due to infinite

naEr- e
-
⑧ r
wirele
+
# =

-------
+ B E
+
+ =

Tr long charged a
I=
!
I
+ · s #
Temp Coefficient
.

t
" tt
R G
=

R Ro -

> ++ I A # Principle of potentiometer RolT-Tol

E= E k r= R E k
Y i
=
=

R,
O UR
=
=

S B 9
R2
# Principle of Meter
Electric Potential & Capacitance bridge #Combination of identical cells
(length of i = nE
PitEor L, wire) series
Electric Potential & Potential Axial ->Y=
R
=

V =

n-cell
·
+ ur
4iEt queto "dipole Equatorial -> x
=
0 100-4
i=
Parallel
Electric Potential Energy At
any point
-> v = Pcoso #
Joule's Law m-cell
mRtr
(For two Chargeit 48r2 iRt
92
H= Joule
Mixed i =

mnE
Capacitance C
0, 02
=

H L It
mRt nr
Calories
=

Relation between EC
-

series combination
-

Parallel Comb 4 18
=- /E
:

.
d
E Or
s
=
-

, 2
Cp =
2
,
+

Capacitance of Parallel Plate Capacitor spherical Capacitor

Ming
OVl
Charges and Magnetism
Air filled Partially filled with dielectric 45. ab
=

I get
Magnetic Force
e

-
I b a Y
-

1=80A c
o = -k C= 4 En q (TxB)
=

# if inner grounded b-a

completely filled
,
Filled with Metal
Capacitance of Isolated Sphere Pitch(P)= 2 My COSO
C= ⑰
C
kE0 qB
=

E
= 4io -a
 charge in Uniform
transverse Magnetic Fitti
Motion of B UH Mr H Ganss's law for Magnetism
= =

Fin= qVB . No
2
=
My =

e
I q =
I 5 15 . = 0
Up 1 + Xm
=

all area
⑭ Radius of Circular path ·
Magnetic Force on a current elements

r =
=m=I= 1 mR may carrying conductor the
Magnetic Field at a point due to magnetic dipole
E i(x5)
Meet
MoM
=

Baxial Beg
=

4str (r2+ 1232

⑭ Biot Savart's law

M itsino-rat
aB =
centre B =

Mi
e or
Baxia, Mits
2M or
Beg = At s

Electromagnetic Induction
M Fat a pointO BENa Nate Magnetic Flux
.

④Force blu two current -onal Emf.

Moll
e ①= B E ing
Bod Rotall
carrying parallel straight For rod For Disc
.

coil carrying .

Conductor P= BACOSO X X X X X
w

mete
w

xxe
X X ⑳
X X

# Ampere's Circuital law x

M2
e v
F = 2h Induced emf
X X X X

X X x x X

&5 d Moi 3=
de
3 Busino
=

. = -
2

121 Buh 151 e

But
= =

or
191= BUI 2

# Magnetic Field due to L Si

an
infinitely long straight wire of A C Generator
Bi
.

F
radius a! Carrying Current : at a point P=
Be & E. sincut 3.= NBAW
= =
.
-

Inductance induced in the coil =-Ldi

B M Moi EMF
=Mo
=
ra B a B=

r> A ,

CITA2
,
r
C
coefficient of self induction
It
self inductance of solenoid
a
long
Torque on a Current Carrying (oil
Moving Coil Galvanometer 14 -
=

= MoUUAl =

MoMrNA
placed uniform dildt
in a
magnetic I <O Or I GO
=

Mutual Inductance
L
field =NIABsinc coefficient of
.

M N2P2
-

Ez 1 M
where k
= -

G R
=

galvanometer
=

MBSiO
=

=
=
=

coupling
Or
NAB Constant ·
I didt didt 12 22
For
, ,

⑪Galvanometer Conversion into voltmeter Mutual inductance of two long solenoids

perfectcontina
> .

into Ammeter M MoMrKr,z) MoMrN , NzAl

=

-
=

i
L

se
Combination of inductors -
Magnell Energy
Series (g 4, the+1s In inductor U=
1 Li2
=

Parallel (p=1 12 M2
sensitivity
-

In BAL
-

4 + 12 +
2M In Solenoid UB=
⑪ Current Sensitivity *
Voltage Sensitivity if coils are far away
Ig P
1
AA
= =
NAB =

Magnetic
=

then
E iR
M=0 ,
SO
energy density Mi= EBs
+12 0 (p= 112 Mi =
12
Magnetic field due to a Current
Carrying Solenoid .

,+ 12 2 Mo

B =

Moni=(oNil/l h =

Mc · Induced Electric Field induced charge flow

-NAD
GE =-d=-AdB O $9= 1Dt=

Magnetism
.

& Matter E
# Bar Magnet as an Equivalent Solenoid .

where m magnetic moment Alternating current

=

B = M. 2m
of solenoid M =

n (21) i lita? R M S value of Current

4/23 Alternating Current &
voltage
.

. .

"msI
⑧

i I sincut Yoms Y
=
=

Potential energy of curie's law

Alternating Voltage
Magnetic dipole -> Fordia Xm47 x =

V sincet irms= 0 707 % Yoms= 0 707 No

. .

U= -

MBCOSO ->
For Paramagnetic
⑰ B Reactance
u
xmCI Mean value of Current & Voltage
=
- -

X= YwC
X- iay= 2% Yay =
0 637 No
I Xm= (w
=A #
= .

I
->
For Ferromagnetic ⑧

1
=
0 637
.
% Yay 0 637 No
:

xm !
al
u =

Mo(1 Xm) +

+ To
Series (CR Circuit I is same for R , RAY OPTICS
C
U= 1
R L
18 C ·
Mirror formula Refractive index
X A Sinc
if VY, then

X
V
-

I 4 ↓u i *
=

Sin
·

Y-V
In U
= =
+

"I
-

- Ye "I for Mirror Forcens For Prism

sinct-b magnificall-on -

SA
+
2 e
xxs
I I then
=
=

u=
I I
2 E, sincut m
=

tang=
=
=

,
2
=
1R+ (X: Xc)2 -

For mirror
thin lens formula Prism of small angle
Power in ac Circuit Resonant series LCR Circuit m=I= -1
.

A
S (l-1) A
I Ii
=

=
Pax =
Erms IrmsCOS4 XXc then z= R
Cens Maker's Formula
·
or I
=

MAX Muns
Par E. . COSd surfaces

= 11(z)
=

(M-
#

Refraction at spherical
2 Resonant frequency Real & apparent depth
* u
- =

power factor Wr =
1 -Factor M =
depth
real

ITC #Power of Lens combination of Lenses

cosb R/2 apparent depth
I
=

q =
if d 0

Pet Item,
P= P
=

, P2-dP, P2 P P+
Transformer ratio
=

, Pz
#
Step-up Transformer
#

Position No of
360
:

Simple Microscope
Reflecting n =

images
E Ip =As
= e
Final I of Object
Es Ep ,
I
s IpGNs Np M=1t, image at Telescope .

y= output power = Es Is step down Transformer M =

D/A " "at 0 M

=to 12 evenanywheree
Esp , Is Ip & Ng <Np Compound Microscope asymmetric n
input Power EpIp
M= MoX Me
Astronomical Telescope Terrestrial Telescope
Alternating Voltage to at
Applied
-I e) image nite) image
in =

It
+
M=
Resistor only capacitor Inductor only
- imageat
M=
E =

Esinct E Esincot 2 =

E.sinct
M=-t imageatd= fot
4f+f
=

e
I =

Isinct I Isin(wt+y) =
I=
Isin(t- 2) /

EM Waves WAVE OPTICS

Displacement equations
herenceof light 1,
Current Maxwell's
Gauss's Law For electrostatics
Iz 2 II, Ee Co e
#

Ig 2, dDE
⑧E
=

. d5 = 9
It #Imax (I +Ez)
o
# Imin= (I, -Ez
E M Waves
.
# Gauss's law for Magnetism ,

55 d at P ;
0 St, 415, at it, 355, 54 ----
⑧
=
=
E E.sin(kx-cut) 0
= =
---
.

B =

BosinCkntcut) #Faraday's law of EMI For I

, Iz= If YDSE
FeM wave
propagating &E 4 I. COS /
B =

x
dt=
de IR YnB= n (2nx
=
. -

along the direction .

W I alPD=nx Bright
Ems O C= E, #Maxwell- Ampere's Circuital Law =

e.e
c= =

Bris Bo
-
2

05 . d =

Mo/I ,E] +2

Er=cBo # Intensity (I) I Energy

Er Diffraction due to a single slit
#

*E
=

I nx Time
~ condition for t
secondary maximum #Freshel distance
=

↓ momentum (P) 2
oo Radiation Pressure
#

P D= asinOn= (2n+1 3,
=
. n
=
1 2 2
, ,
=
----

3x108m/ s e N e ro m u s c energet
c
=

a c u s e re r aweabsorbinsta
condition for

er
th
secondary minim e
4I .
=

asiOn= nx n =
1 , 2, 3 , -----

I B * idth of central Maximum

xD
=

Cx
=

Energy density
#Angular fringewidth #Angular fringe width of secondary

U E Vi =

1 (UEaEE (UlaBo -

Mo
of central maxima=
2
Maxima or
minima: I
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R = R 0 A"' .J = mas� 61- nucJe.a.u
voh.unt at- nutl ws
� MQ�S- defect-
Ml=r?lmp + (A-Z)m,}- mN]
• 6fnd�n9 enirg�
S·E= 6mG2,.
• 0E = Sf /A C 6�'!n�fl89 Pf.tJ
semiconductor Devices
• 'rotal Ct.urtn� throl13h the.. pl1re
.f.em1 conduci-Or
- _¼_ _Ih I
I I_=
--,
-t

# No· of o.lpha pa.rt, cles • tltctritol Cond.uttvthf fn !uni C.OnducJ-or

0

scattered per u.nit areQ. @Potentia.l energy at -/he ea

N(0) oc_l - u=n -2+•2- z eV
2.
2.
r= e( ne, ...«t -t- nh Jle.,)
5in4 (e/2.) n
# Impact Para.meter
� Tota.I &ne�� of eE:J ..tt = mobt l!� ·
o;, = iN,1 a,.
="""'
b= ze2·cot (e/1) Eh -13·�2.-Z:-eV -ll<n-= --E nl
4JCEr,K h
LJ,, = 2, e., = -21(.,, � =- eN.a .ue,
K= kine�c eneJGS� oPJcequenc8 of electron fn +he nth
z :-: atomic /\Jwnber-
-0. = -1 2.4J/;le4m = 6•G2.x1d5z2.
:tt:-Disto.nce of closest approoch n (41tE,) rf h3
r.0 = Z- Ze
J!. n3
� Wo.velen<Hh of ,tQd.•1atoion a1n ...u.111e
4;c.f.K "h o o
f
.L
1;rom,1 1ori rom n.i ---P n,
.l] �
# BOHR'S MODcL
[ .!..1. - :i. �=R�b i's
1
w AnQ11lor
a momentum of e
e
.L = �z:
L= nh or mvr= nh )\ hI n:a. '\.= o.1 •uuXIO
--r.
an.
:f-1
:l.JC :be ber of-- .s
tNlUTl pectral Lines due -lo
eFrequency of rodfatfon tra.nsiil�n of e from n-lh Orbit to
0

.,:,= e�-s. lower orbit 1s •

h N= n(n-1)
� IBoh r's formulae I z
Rodfus of ntti Orbft # Ioni%a.h°on ene,e3� _,. l3·G eV
r., =4Jrean2.L1 ri = 0•63 n A
2. o n2.
�Jr. mZi
2
z * Ioni�atl'on ----. 13-G z V
1

@ veloci1H - of ee ,,2.
G
vn = - 1 2Jt::te
- = 2�z
1

-4JtE.0 n h 11
a �ine��c ene"8�
�= 13,6Z1 eV
n'-