Physics quick revision on last minute for class 12 term 1, full and detailed notes for last minute revision and before exam glance, only 10 min per chapter.

1. ELECTROSTATICS
Electric Field Intensity:- 2
0
1 Q
E
4 r
=

vector unit:-
N
C
dV
E
dr
= − Electric Potential
0
1 Q
V
4 r
=

scalar unit:-
J
C
V E.dr
= −

Electric Dipole:- Equal and Opposite charge separated by small distance, Dipole moment P 2ql
= vector(direction from negative to positive charge unit:- C m
E & V on Axial Line:- E at pt. P on axial line
is ( )
B A
E E E
= + −
( ) ( )
= −
 
− +
2 2
0 0
1 q 1 q
E
4 4
r l r l
( ) ( )
 
= −
 
 
 − +
 
2 2
0
q 1 1
E
4 r l r l
( ) ( )


= =
 −  −
2 2
2 2 2
0 0
2 2qrl 2pr
E
4 r l 4 r l
=
 3
0
2P
E
4 r
For short dipole r >> l (direction (-)
to (+))
( ) ( )
−
= + = +
 
+ −
A B
0 0
1 q 1 q
V V V
4 4
r l r l
( )
=
 −
2 2
0
1 P
4 r l
 =
 2
0
P
V
4 r
E & V on Equitorial line:-
( )
=  + 
=
 = 
 
=    =
 
  
= =

 +
A B
A B
A
2
0
3 3
2 2
0
0
E E cos E cos
since
E E
E 2E cos
1 q l l
E 2 cos
4 x x
x
2ql P
E
4 x
4 x l
( )
=
 +
3
2 2 2
0
P
E
4 r l
( )
=
 3
0
P
E
4 r
For short dipole r >> l
Direction (+) to (-)
( )
−
= + = + =
 
A B
0 0
q
1 q 1
V V V 0
4 x 4 x
Torque on Dipole:- Net force = +qE – qE = 0
Torque = Force × ⊥ distance
= qE × BC [BC = 2l × sin θ
= qE 2l sin θ
= E (2ql) sin θ
τ = PE sin θ = P E

τmax = PE for θ = 90o
work done in Rotating Dipole
( )
W d 1 cos PE
=   = − 

Energy of Dipole: U = –PE cos θ
Stable equilibrium θ = 0, U= –PE
Unstable equilibrium
Θ = 180o
⇒ U = PE.
Gauss Theorem:- Total electric flux (total no. of lines
of forces) emerges from closed surface is
0
1
times the
charge enclosed =

 in
0
q
E.dS
E due to long charged wire:
Linear charge density  =
q
l
=

 in
0
q
E.dS
+ + =

   in
1 2 3
0
q
E.dS E.dS E.dS
For dS2 and dS3 θ = 90o
For curved surface dS1 θ = 0
 =

 0
q
E dS ⇒ ( )
 =
0
q
E 2 rl
= =
   
0 0
2q
q l
E
2 rl 4 r
⇒

=
0
1 2
E
4 r
E due to charged plane sheet:
Surface charge density  =
q
A
For non conducting plate charge is on both side
=

 0
q
2 E.dS
=
0
q
2EA
=
0
q
E
2 A

=
0
E
2
For conducting sheet

=
0
E
* E is independent of distance from the sheet.
E due to charged Hallow Sphere:
Volume charge density  =
q
V
=

 in
0
q
E.dS
 =

 0
q
E dS
( )
 =

2
0
q
E 4 r
=
 2
0
1 q
E
4 R
On surface
=
 2
0
1 q
E
4 r
Outside & =
E 0 as q = 0 inside
Capacitor:- Q = CV unit:- Farad, * C depends on dimensions
Capacitance for parallel plate
capacitor
Consider || plate capacitor with
area of plate A, capacitance C and
dist. b/w plates d
= =

Q Q
C
V E d

=
0
E for charged sheet
 =
Q
A
for surface charge density


= =



0
0
A
A
C
d
d
If dielectric with dielectric
constant k is filled b/w the plates.
C’
= kC
Surface charge Density
 =  = 
Q
Q A
A
Electric field
= +
air dielectric
E E E
 
= +
 
0 0
k
Potential V = E × d
( )
 
 = + +
 
0 0
V a b t
k
 

= + +
 
  
0
t
V a b
k
 

= − +
 
  
0
t
V d t
k
Now 
= =
 

− +
 
  
0
Q A
C
V t
d t
k
Energy of Capacitor
Energy = work done in bringing charge
at potential V
=  =
q
dW V dq .dq
C
 
 
= =  = =
 
 
Q Q Q
2 2
0
0 0
1 1 q 1 Q
U dW q dq
C C 2 2 C
= = =
2
2
1 Q 1 1
U CV QV
2 C 2 2
Energy Density (energy per unit volume)
( )


= = = 

2
2 0
2
0
A
1
1
E d
CV
1
2 d
2 E
volume A d 2
Unit of energy density:- J/m3

2. CURRENT ELECTRICITY
Electric Current:
q
i
t
= , unit - Ampere
* Scalar quantity nAle
i q / t
t
= =
Current I = neAVd
eV
I neA
ml

=
2
I ne A
V ml

=
V = IR
2
V ml
R
I ne A

= =
Mobility d
V
E
 = (m2
/sV)
A – Area
n – number of free electrons in unit volume
resistivity ρ =
RA
l
ρ 2
m
ne 
=
Also J E

=
I
J
A
= = current density (vector)
Drift velocity:- v u a
= +
if u = 0
–14
relaxationtime (10 s)
 −
d
V a
=
Also ma = eE = f
eE
a
m
 =
d
eE
V
m

= (10–5
m/s) as V = Exl
d
eV
V
ml

=
Temperature dependence of resistivity Electric Energy & power Colour Coding of Resistor
with increase in temperature
conductors : decrease. inc.
semiconductors; n increase dec
 

 





Power = Energy / Time = Work done / Time
It is a scalar quantity
2
2 V
E V.I.t I Rt t
R
= = =
2
2 V
P V.I I R
R
= = =
1 unit = 1 KWh
Series combination of resistance:- R = R1 + R2. Current same
Parallel combination of resistance:- 1/R = 1/R1 + 1/R2 Voltage same
E = V + ir charging
E = V – ir discharging
KIRCHOFF’S LAW
i. i = 0 Junction law
ii. iR = E = 0 Voltage law
Cell in series I = nE /nr + R
Cell in parallel
nE
i
r nR
=
+
Meter Bridge:
Let Unknown Resistance = X
R l
X 100 l
=
−
R(100 R)
X
l
−
 =
Resistivity
RA
L
 =
Meter bridge in most sensitive when null pt. in middle.
Wheatstone Bridge:
Balance condition P / Q = R / S
Potential at A & B same at null pt.
Position of Galvanometer &
battery can be interchanged at null pt.
Potentiometer:
Principle:- If constant current flows through wire of uniform cross section, then drop in directly proportional to length of that portion
E
K
L
= = Potential gradient
When K1 inserted then E1 = K × L1
When K2 inserted then E2 = K × L2
1 1
2 2
E L
E L
=
When only K1 is inserted then E = K × L1
When K1 and K2 both are inserted then
V = K × L2 = E – r
1
2
1
l
r R
l
 
= −
 
 
Advantage of Potentiometer over voltmeter:-
1. Preferred over voltmeter as it give exact reading draw no
current
2. Sensitivity increase with increase in length
3. A small P. D can be measured accurately with the help of
potentiometer. The resistance of voltmeter is high but not
infinity to work as an ideal voltmeter.
4. The internal resistance of a cell can be measured with the
help of potentiometer.

3. MOVING CHARGES & MAGNETISM
Magnetic Field:- Produced by magnet, moving charge, Vector quantity. Unit:- Tesla (weber/m2
), gauss (maxwell/cm2
) IT = 104
G
Oested Experiment:- Current carrying conductor produces magnetic field.
Bio Savart Law:- It gives M.F. at a point around
current carrying conductor.
idl sin
dB
r
 
=

0
2
4
TmA
− −

=

7 1
0
10
4
μ0 – Permeability of free space
Direction of B:- Perpendicular to dl and r.
B = 0 if sin θ = 0
B = max sin θ = 1 θ = 90o
Vector Form
idl r
dB
r
 
=

0
3
4
Ampere’s Circuital Law:- B.dl i
= 
 0 The line integral of magnetic field B for
any closed circuit is equal to μ0 times current i threading through this closed loop
and this closed loop is called Amperian loop.
B. Due to Infinitely Long Wire:-
Magnetic field at P due to wire
B.dl i
= 
 0
B dl i
= 
 0
B(2πr) = μ0i
l
B
r

 =

0 2
4
Direction:- Right Hand Thumb Rule curly finger gives field direction if thumb of
right hand points current outside
Mag. Field At Centre of Coil:-
o
idl sin
dB
r

=

0
2
90
4
i
B dB dl
r

 = =

 
0
2
4
( )
i
r
r

= 

0
2
2
4
i
B
r

= 0
2
or
Ni
B
r

= 0
2
Direction:- Right Hand Thumb Rule.
B. due to Solenoid:-
Bdl B.dl cos
= 

N – Total Turns
d
a
B.dl i
= 
 0
( )
b c d a
a b c d
B.dl B.dl B.dl B.dl Ni
+ + + = 
    0
( )
b
a
B.dl Ni
+ + + = 
 0
0 0 0
b
a
B. dl Ni
= 
 0 B.L ni
= 0 ⇒ ∴ B = μ0ni
N
n
L
= (Turns per unit Length)
On Axis of Coil:-
o
idl sin
dB
x

=

0
2
90
4
B dB sin
 = 

( )
i a a
.
x
x
 
=

0
2
2
4
( ) /
Nia
B
a r

=
+
2
0
3 2
2 2
2 Force on charge in Electric field:-
F = qE (both for rest & motion)
Magnetic Field:-
F = qV Bsin θ (only for moving charge)
B. Due to Toroid:- (Closed solenoid)
B.dl Ni
= 
 0
( )
B r Ni
 = 0
2
Ni N
B n
r r
  
= =
 
 
 
0
2 2
B ni
= 0 [at P]
Lorentz Force:- F = qE + qvB sin θ = q (E + vB sin θ)
Cyclotron:- Used to accelerate charge Particles.
Principle:- The repeated motion of charged particles under mag. & ele.
field accelerates it. E.F. provides energy while M.F. changes direction.
Construction:- Dees, Sources, M.F., R.F. Oscillator
Working:- max
Max KE mv
= 2
1
2
qBr
m
m
 
=  
 
2
1
2
q B r
K.E.
m
=
2 2 2
1
2
Force b/w 2 parallel current carrying wire:- Force acting on a due to b.
o
i
F i l sin
r

 
=  

 
0 1
2
2
90
4
i i
F
r

 
=  

 
0 1 2
2
4
(For unit Length)
By Flemings LHR force is of attraction for same
direction of current and force of repulsion for opposite
direction of current.
if i i A, r m.
= = =
1 2 1 1
then F = 2 × 10–7
N.
Current Sensitivity:- Deflection per unit current
s
BAN
I
i C

= =
Radian
Ampere
Moving Coil Galvanometer:- Device
to detect & measure electric current.
Principle:- Current loop experience
torque in uniform M.F.
Construction:- Light Coil, concave
magnetic Poles → radial field.
Theory:- Deflecting torque
= Restring force (torque)
B × i × N × A × sin θ = CØ
(θ = 90o
) as field is radial
∴ B AiN = CØ ⇒
C
i
ABN

=
Torque Experienced By a
Current loop in uniform
Magnetic Field:-
τ = F × ⊥ distance
= Bil × bsin θ
τ = Bi A sin θ
For N Turns:-
τ = BiNa sin θ
Voltage Sensitivity:- Deflection per unit voltage
s
s
I BAN
V
R V iR CR
 
= = = =
Radian
Volt
 
 
 
Limitation:- Only charged particles can be acceleration
For circular path:-
mv
qvB
r
=
2
⇒
mv
r
qB
= ⇒ r ∝ v
q B r
K.E.
m
=
2 2 2
1
2
Time period = Distance / Velocity = 2πr / v ⇒ T = 2πm / qB
Frequency of Revolution:- f = 1/T = qB/2πm
Application:-
For nuclear
reaction & other
research purpose.

4. Conversion of Galvanometer into Ammeter:-
(i – ig)S = ig.G
g
g
i .G
S
i i
 =
−
{For Ideal Ammeter R = 0}
Conversion Into Voltmeter:- By connecting high resistance in series
{For Ideal voltmeter, R = ∞}
( )
g
V i R G
= +
( )
g
V
R G
i
= +
ELECTROMAGNETIC INDUCTION (E.M.I)
The phenomena of producing induced current due to change in magnetic flux is called electromagnetic induction.
Faraday Law:- (i) Change in magnetic flux induces current which last till there is change.
(ii)
d
e
dt
− 
=
Lenz’s Law:- Induce current opposes the factor due to which it is produced.
acc. to law of conservation of energy.
Method of producing emf:-
d dBAcos
e
dt dt
−  − 
= =
Induced current / charge:-
d e d dq d
e ,i ,
dt R Rdt dt Rdt
−  −  − 
= = = =
d
dq
R
− 
=
Motional emf:- The emf induced due to motion of a conductor in M. field.
Motional emf:-
d
e
dt
− 
=
dB.A
dt
−
=
BdA Bldx
dt dt
− −
= =
e Bvl
= −
Direction = Anticlockwise
Force:-
Bvl
i
R
=
Bvl
F Bil B l
R
 
= = −  
 
B vl
F
R
−
=
2 2
Power:- P = Fv
B v l
P
R
−
=
2 2 2
Rotating rod:-
d
e
dt
− 
=
dBA
e
dt
−
=
BdA
e
dt
=
B L
e

=


2
2
e B L
=  2
1
2
or e B R
=  2
1
2
No. of spokes is increased emf remain same.
Eddy Current:- The circulating induced
current in a oscillating metallic block kept in
magnetic field. In can be reduced by using
laminated core, or cutting slots in block.
Application:-
(i) Magnetic brakes
(ii) Induction furnace
(iii) Dead beat galvanometer
Self – Induction:- Change in current in a coil, induced
current is produced which opposes the change in same coil.
Unit:- L = 1 Henry (H)
Dimension Formula:- [ML2
T–2
A–2
]
Solenoid:-
ϕ = Li
ϕ = BAN = (μ0niA) × N
Li = μ0n2
× i × A × l (n = N/l)
L = μ0n2
Al
Mutual – Induction:- when the change in current
in primary coil induces current in secondary coil.
ϕ ∝ i
ϕ = Mi
Unit – Henry
∈0 = Farad/m
μ0 = Henry/m
Solenoid:- B2 = μ0n2i2
ϕ = B2AN1
ϕ = (μ0n2i2)AN1
ϕ = Mi2
Mi2 = μ0n1n2Ali2
M = μ0n1n2Al
*No. of turns is double than inductance
become four times ( L ∝ n2
).
Electrical Resonance:-
F
LC
=

1 1
2
Power in A.C. circuit:-
P V i cos
= 
0 0
1
2
V i
P cos
= 
0 0
2 2
 
RMS RMS
P V i Cos
= 
R
Cos
Z
 
 =
 
 

5. MAGNETISM & MATTER
Properties of Magnet:
1. Magnets have north pole and south pole.
2. Likes poles repel & unlike attract each other.
3. Freely suspended magnet rests in N – S direction.
4. Monopole do not exist.
5. Mag. Length is eq to 0.84 times of their geometric
length.
Permanent Magnets are made up of steel:
Hysteresis Loop / curve: The graph plotted b/w
external field (H) & mag. induction (B) is called “BH
curve ‘or hysteresis Loop.
Energy Loss: Work done (energy loss) in
magnetization and demagnetization is eq. to area of
BH curve.
Magnetic Material:
Paramagnetic
1. odd no of e–
in outer most
orbit &
possess net
dipole
moment.
Diamagnetic
1. Even no of
e– and
possess net
dipole
moment is 0.
Ferromagnetic
1.
Ferromagnetic
materials
have some
unpaired
electrons so
their atoms
have a net
magnetic
moment. They
get their strong
magnetic
properties due
to the presence
of magnetic
domains.
Magnetic Dipole Moment: N 2l
 → S
M = m2l unit: Am2
m → pole Strength.
M → Magnetic Dipole Moment
Elements of Earth’s magnetic field:
1. Angle of Dip: Angle b/w horizontal line & mag.
meridian as a freely suspended magnet.
2. Angle of Declination: Angle b/w geographical
meridian & mag. meridian is called Angle of
Declination
3. Horizontal Intensity of Earth Mag.
The horizontal component of to. Earth’s field at any
point is called horizontal intensity
( )
2
2 2
V
H V
H
B Bsin
tan ,B (B ) B
B Bcos



= = = +
2 2
H V
B B B
= +
M. Due to Current Loop: When current is passed
through a loop it, behaves like a magnet. (M = iA) =
current × Area, M = NiA
⸫ 2
q evr
M ( r)
t 2

= = {for e-
, v = 2r/t}
Magnetic Dipole Moment of a revolving:
( )
2
q
M iA r
t

= = =
evr
2
{for e-
, v = 2r/t}
2. Aligns || to
field & get
weakly
magnetized
along ext.
field.
2. Align ⊥
to ext. field.
2. When
a magnetizing
force
is applied, the
domains
become aligned
to produce a
strong magnetic
field
within the part.
Magnetic Field Intensity due to magnetic Dipole:
1. On Axial line: 0
3
2M
B
4 r


=
2. On Equatorial line: 0
3
M
B
4 r


=
Magnetic Field of Earth:
Torque Acting on dipole in Mag. field:
f dis.
 =  = mB2 l sin = m2 lBsin
= MBsin
⸫ MBsin
 
=
→Torque is ⊥ to mag. field and mag. dipole
moment (M)
→ max
 = MB (sin = 1),  = 90° {Due to torque
rotation motion or liner. }
→ min
 = 0 = (sin = 0) ,  = 0
3. Mag. field
pass through
substance
4.Increase
with decrease
in temp.
3. Mag. field
repelled by
substance.
4. Increase
with increase
in temp
3. Temp. at
which
ferromagnetic
substance
becomes
paramagnetic
called curie
Temperature.
Work done in Rotating the Dipole:
W = MB [cos1 – cos2] Electromagnets: Are prepended by passing electric
current in a solenoid. The magnet lasts till the current
is passed.
It can be increased by:
1. Increasing number of turns.
2. Increasing current.
3. using soft iron core.

6. ALTERNATING CURRENT (A.C)
TRANSFORMER: - It is a device use the
change AC voltage.
Principle: It is based on principle of mutual
induction.
Construction: two coil primary & secondary
Step up: Increase voltage (k>1) and decrease
current.
Step down: decrease voltage (k < 1) and
increase current.
Theory:
p
s S
p p s
i
V N
K
V N i
 
= = =
 
 
 
100%
output
input

 
= 
 
 
A.C. Generator :- It is a device which convert mechanical
energy into electrical energy.
Principle: It is based on principle of electromagnetic
induction.
Construciton:
(i) Arumature coil.
(ii) Field magnet
(iii) Slip ring
(iv) Brushes .
d
e
dt

−
=
– cos
dBA t
e
dt

=
e = BA(–ωsinωt)
e = BAN ωsin ωt
emax = e0 = BANω
e = e0sinωt
Alternating Current: -
D.C – Direction & magnitude are fixed.
A.C – Change in both magnitude and direction.
HALF– CYCLE:
0
V
Vavg.


= 
avg 0
0
1
V . V sin d

 

= 
 
av 0 0
1
V V cos



= −
 
0
av
V
V cos cos0


−
= −
0 0
av av
2V 2I
V or I
 
= =
Full Cycle: Vav =
2
0
1
Vd
2


 
2
avg 0
0
1
V V sin d
2

 

= 
( )
2
0
avg 0
V
V cos
2



= −
( ) ( )
0 0
avg
V V
V cos2 cos 1 1
2 2
 
 
= − + = − +
avg avg
V 0 or I 0
= =
Root mean Square:
2
2
RMS
0
1
V V
2


= 
2 2
2 2 2 2
RMS 0
0 0
1 1
V V V sin d
2 2
 
 
 
= =
 
2 2
2 2
0 0
RMS
V V 1 cos2
V ( ) sin
2 2 2

 

−
 
= = =
 
 
0 0
RMS RMS
V I
V or I
2 2
= =
A.C. Circuit: -
Pure Resistive Circuit: (Circuit containing
resistance)
0
V
V
sin t
R R

=
   
0 0
i i sin t V V sin t
 
= =
V
I
Resistance is independent frequency of A.C.
Pure capacitor circuit (circuit containing capacitor only)
Q = CV
d dV
C
dt dt

= , d
i C
dt
= (V0 sinωt) 0
d
i CV sin t
dt

=
ωCV0 cosωt
0
V
i sin( t / 2)
1
C
 

= +
0
V
i
1
C

=
Pure inductive circuit:
V = V0 sin ωt
Ldi
V
dt
=
Vdt
di
L
+
=
0
V sin tdt
di
L

=
( )
0 0
V V
di sin tdt cos t
L L
 
= = −
 
Series LCR circuit: -
2 2 2
R
v V (Vc Vc)
= + −
2 2 2
L C
(IZ) (IR) (IX IX )
= + −
2
2 L C
Z R (X X )
= + −
2
2
1
Z R L
C


 
= + −
 
 
1
L
C
tan
R



 
−
 
=
 
 
 
 
⇒ L C
X X
tan
R

−
 
=
 
 