Physics Formulas

Formulae Sheet for Physics www.concepts- of-physics.com | pg.
Physics formulas from Mechanics, Waves, Optics, Heat and

Thermodynamics, Electricity and Magnetism and Modern Motion in a straight line with constant a:
Physics. Also includes the value of Physical Constants. Helps
v = u + at, s = ut + 1
at2, v2 − u2 = 2as
in quick revision for CBSE, NEET, JEE Mains, and Advanced. 2
0.1: Physical Constants Relative Velocity: →vA/B = →vA − →vB
Speed of light c 3 × 108 m/s

u
Planck constant h 6.63× 10−34 J s y
hc 1242 eV-nm x
u sin
H
Gravitation constant G 6.67× 10−11 m3 kg−1 s−2 Projectile Motion:
θ
θ
Boltzmann constant k 1.38× 10−23 J/K O u cos
Molar gas constant R 8.314 J/(mol K) θ R
Avogadro’s number NA 6.023 × 1023 mol−1
1 2
Charge of electron e 1.602 × 10−19 C x = ut cos θ, y = ut sin θ − 2 gt
g
Permeability of vac- µ0 4π × 10−7 N/A2 y = x tan θ— x2
uum 2u cos2 θ
2
Permitivity of vacuum ϵ0 8.85 × 10−12 F/m 2u sin θ u2 sin 2θ u2 sin2 θ
Coulomb constant 1 T= , R= , H=
4πє
0 9 × 109 N m2/C2 g g 2g
Faraday constant F 96485 C/mol
Mass of electron me 9.1 × 10−31 kg 1.3: Newton’s Laws and Friction
Mass of proton mp 1.6726 × 10−27 kg
Mass of neutron mn 1.6749 × 10−27 kg Linear momentum: p→ = m→v
Atomic mass unit u 1.66 × 10−27 kg
Atomic mass unit u 931.49 MeV/c2 Newton’s first law: inertial frame.
Stefan-Boltzmann σ 5.67×10−8 W/(m2 K4)
Newton’s second law: F→ = dp→
dt , F→ = m→a
constant
Rydberg constant R∞ 1.097 × 107 m−1 Newton’s third law: F→ = −F→
AB BA
Bohr magneton µB 9.27× 10−24 J/T
Bohr radius a0 0.529× 10−10 m Frictional force: fstatic, max = µsN, fkinetic = µkN
Standard atmosphere atm 1.01325× 105 Pa 2 2
Wien displacement b 2.9 × 10−3 m K Banking angle: v
= tan θ, v
= µ+tan θ
rg rg 1−µ tan θ
constant
Centripetal force: F = mv 2
, a = v2
c r c r
1 MECHANICS Pseudo force: pseudo

= −m→a , F
0 centrifugal r
mv2
=−
F→
1.1: Vectors Minimum speed to complete vertical circle:
√ √
vmin, bottom = 5gl, vmin, top = gl
Notation: →a = ax ˆı + ay ȷˆ+ az kˆ
q
Magnitude: a = |→a| = a2 + a2 + q
x y z θ
l cos θ l
Conical pendulum: T = 2π
a2 θ T
Dot product: →a ·→b = axbx + ayby + azbz = ab cos θ g
ˆı mg
→a × →b
Cross product:
→b
kˆ ȷˆ
→a
1.4: Work, Power and Energy
→a ×→b = (aybz − a z b y )ˆı +(azbx − axbz)ȷˆ+ (axby − ∫
Work: W = F→ · S→ = FS cos θ,W = F→ · dS→
a y b x )kˆ
2
Kinetic energy: K = 12 mv2 = 2m
p
|→a × →b| = ab sin θ

→aav = ∆→v/∆t →ainst = d→v/dt
1.2: Kinematics
Average and Instantaneous Vel. and Accel.:
→vav = ∆→r/∆t, →vinst = d→r/dt
Get Formulas www.concepts-of-physics.com Get Our Book

⃝c 2020 by Jitender Singh Ver. 2020 ~
Formulae Sheet for Physics www.concepts- of-physics.com | pg. 2
Potential energy: F = −∂U/∂x for conservative

forces.
Ugravitational = mgh, Uspring = 1 kx2 2
Work done by conservative forces is path

indepen- dent and depends only on initial
H
and final points:
F→conservative · d→r = 0.
Work-energy theorem: W = ∆K

Mechanical energy: E = U + K. Conserved if forces are

conservative in nature. Rotation about an axis with constant α:
ω = ω0 + αt, θ = ωt + 21 αt2, ω2 − ω02 = 2αθ

Power P = ∆W
, = F→ · →v
P
av ∆t inst
Σ ∫
Moment of Inertia: I = 2
i m i ri , I= r2dm
1.5: Centre of Mass and
Σ Collision
xm i i ,
xdm 2 1
mr2 2 2
Σ ,
Centre of mass: xcm = , xcm = dm mr2 1
2
mr2 2
3
mr2 2
5
mr2
1
12 ml
2 mr 2 m(a +b )
12
mi
solid rectangle
CM of few useful configurations: ring disk shell sphere rod hollow
m1 r m2 b
a
1. m1, m2 separated by r: C
m2 r I
m1+m2
m1 r Ic
m1+m2
Theorem of Parallel Axes: I = Icm + md2 d
cm
2. Triangle (CM ≡ Centroid) yc = 3h h
C
h
3
z y
Theorem of Perp. Axes: Iz = Ix + Iy
2r x
3. Semicircular ring: yc = π
C
2r
r π
√
4. Semicircular disc: y = 4r Radius of Gyration: k = I/m
c 3π C 4r
r
Angular Momentum: L→ = →r × L→ = I ω→
3π
p→,
5. Hemispherical shell: yc = r
C r
r 2 y
dtdL→ P θ →
Torque: →τ = →r × F→ , →τ =
2 F
, τ = Iα
→r
6. Solid Hemisphere: yc = 3r
O x
8
r
C 3r
8
Conservation of L→ : =0 L→ = const.
ext
→τ =⇒
7. Cone: the height of CM from the base is h/4 for Σ Σ
Equilibrium condition: F→ = →0, →τ = →0
the solid cone and h/3 for the hollow cone.
Kinetic Energy: Krot = 1
2
Iω2
Σ Dynamics:
Motion of the CM: M =
mi
F→
→τcm = F→ext = p→cm = m→vcm
Σ 1 2 1m→acm2, →
Icm α→ ,
→vcm =
mi →v
i
p→
cm = M →v
cm , →a
cm =
ext
, M M K= 2
mvcm + 2 Icmω , L = I cm ω→ + →rcm ×
∫ m→vcm
Impulse: J→ = F→ dt =
1.7: Gravitation
∆p→ Before collision After collision
Collision: m1 m2 m1 m2 m1 F F
Gravitational force: F = Gm1rm2 2
v1 v2 v1′ v2′
Momentum conservation: m1v1 +m2v2 = m1v1′ +m2v2′
Elastic Collision: 21 m1 v1 2+12 m2 v2 2 = 21 m1 v1′ 2+12 m 2 v2′ 2 Potential energy: U = − GMm
r
m2 r
Coefficient of restitution:
Gravitational acceleration: g = GM
−(v1′ − v′2) 1,
R2
v 1 0 completely elastic
e= —v
2
= , completely in-elastic Variation of g with depth: ginside ≈ g 1 − h
R

If v2 = 0 and m1 m2 then v1′ = −v1. Variation of g with height: goutside ≈ g 1 − 2h

R
If v2 = 0 and m1 m2 then v2′ = 2v1.
Elastic collision with m1 = m2 : v1′ = v2 and v2′ = v1. Effect of non-spherical earth shape on g:
gat pole > gat equator (∵ Re − Rp ≈ 21 km)
1.6: Rigid Body Dynamics Effect of earth rotation on apparent weight:

Angular velocity: ωav = ∆θ
∆t
, ω= dθ
dt
, →v = ω→ × →r
Angular Accel.: αav = ∆ω

, α= dω
, →a = α→ × →r
∆t dt

ω→
A→
Superposition of two SHM’s: A→ 2
mω2R cos є δ
mg θ
mgθ′ = mg − mω2R cos2 θ θ A→ 1
R
x1 = A1 sin ωt, x2 = A2 sin(ωt +

q δ) x q
= x1 + x2 = A sin(ωt + ϵ)
GM
Orbital velocity of satellite: vo = A= A 2
+A 2
+ 2A A cos δ
R 1 2 1 2
q A2 sin δ
Escape velocity: ve = 2GM tan ϵ =
R A1 + A2 cos δ
vo
Kepler’s laws: 1.9: Properties of Matter
a
Modulus of rigidity: Y = F/A
, B = −V ∆P
, η= F
First: Elliptical orbit with sun at one of the ∆l/l ∆V Aθ

focus. Second: Areal velocity is constant. (∵ d L→ 1 dV
/dt = 0). Third: T 2 ∝ a3. In circular orbit T2= Compressibility: K = B =− V dP
2 GM 1
4π
a3.
lateral strain ∆D/D
Poisson’s ratio: σ = =
longitudinal strain ∆l/l
1.8: Simple Harmonic Motion

Hooke’s law: F = −kx (for small elongation x.) Elastic energy: U = 1 2stress × strain × volume
2
d x k
Acceleration: a = dt 2 = − mx = −ω x
2
√ Surface tension: S = F/l

Time period: T = 2πω = 2π
m
k
Surface energy: U = SA
Displacement: x = A sin(ωt + φ)
√ Excess pressure in bubble:
Velocity: v = Aω cos(ωt + φ) = ±ω A2 − x2
∆pair = 2S/R, ∆psoap = 4S/R
Capillary rise: h = 2S cos θ

rρg
U
Potential energy: U = 2 kx 1 2
x
−A 0 A
Hydrostatic pressure: p = ρgh

Kinetic energy K = 21 mv2 K
x Buoyant force: FB = ρV g = Weight of displaced liquid
−A 0 A
Total energy: E = U + K = 1 Equation of continuity: A1v1 = A2v2 v2

1
mω2A2 2
v
Bernoulli’s equation: p + 1 ρv2 + ρgh = constant
2
q √
Torricelli’s theorem: vefflux = 2gh
Simple pendulum: T = 2π gl
l
Viscous force: F = −ηA dvdx
q F
I
Physical Pendulum: T = mgl
Stoke’s law: F = 6πηrv
2π
v
q 4
Poiseuilli’s equation: Volume flow
= πpr
r
Torsional Pendulum T = 2π I
k
time 8ηl
l
2r2(ρ −σ)g
Terminal velocity: vt = 9η
Springs in series: 1
= 1
+ 1
k1 k2
keq k1 k2

k2
Springs in parallel: keq = k1 + k2
k1

q
2 Waves 4. 1st overtone/2nd harmonics: ν1 = 2

q T
2.1 : Waves Motion 5. 2nd overtone/3rd harmonics: ν2 = 3

Formulae Sheet for Physics www.concepts- of-physics.c2Lomµ | pg. 8
2 2 2L µ
y y
General equation of wave: ∂
= 1 ∂
. 6. All harmonics are present.
∂x2 v2 ∂t2
Notation: Amplitude A, Frequency ν, Wavelength λ, Pe-

riod T , Angular Frequency ω, Wave Number k,
L
T = 1 = 2π , v = νλ, k = 2π
String fixed at one end:
N A
ν ω λ A N
Progressive wave travelling with speed v: λ/2
y = f (t − x/v), ~ +x; y = f (t + x/v), ~ 1. Boundary conditions: y = 0 at x = 0

−x 2. q
Allowed Freq.: L = (2n + 1) λ , ν = 2n+1 T
, n =
y 4 4L µ
0, 1, 2, . . ..
A q
x
λ λ 3. Fundamental/1 harmonics: ν0 = 4L1 T
2
q µ
st
Progressive sine wave:
4. 1st overtone/3rd harmonics: ν1 = 3
qT
4L µ
y = A sin(kx − ωt) = A sin(2π (x/λ − t/T ))
5. 2nd overtone/5th harmonics: ν2 = 5
4L µ
T
2.2 : Waves on a String 6. Only odd harmonics are present.
Speed of waves on a string
√ with mass per unit length µ
and tension T : v = T/µ q
√
Sonometer: ν ∝ 1L ,ν T,ν∝ 1
√
µ
.ν= n T
µ
2 2 2 ∝ 2L
Transmitted power: Pav = 2π µvA ν
Interference: 2.3 : Sound Waves
y1 = A1 sin(kx − ωt), y2 = A2 sin(kx − ωt + δ) Displacement wave: s = s0 sin ω(t − x/v)
y = y1 + y2 = A sin(kx − ωt + ϵ) Pressure wave: p = p0 cos ω(t − x/v), p0 = (Bω/v)s0

q
Speed of sound waves:
A= A12 + A22 + 2A1A2 cos δ
A2 sin δ s s s
tan ϵ = B Y γP
A1 + A2 cos δ vliquid =
2nπ, constructive; , vsolid = , vgas =
δ= ρ ρ ρ
(2n + 1)π, 2
B
2
p0 v
2
Intensity: I = 2π
s 2 ν2 = = p0
destructive.
v 0 2B 2ρv
2A cos kx
Standing Waves: x
A N A N A
Standing longitudinal waves:
λ/4
p1 = p0 sin ω(t − x/v), p2 = p0 sin ω(t + x/v)
y1 = A1 sin(kx − ωt), y2 = A2 sin(kx + ωt) p = p1 + p2 = 2p0 cos kx sin ωt
y = y1 + y2 = (2A cos kx) sin
ωt n + 1 λ , nodes; n = 0, 1, 2, . . .
x=
2
2
antinodes. n = 0, 1, 2, . .
n 2λ ,
. L
Closed organ pipe:
L
String fixed at both ends:

N A N A N
λ/2 1. Boundary condition: y = 0 at x = 0

2. Allowed freq.: L = (2n + 1) λ , ν = (2n + 1) v , n =
1. Boundary conditions: y = 0 at x = 0 and at x = L 0, 1, 2, . . . 4 4L

q
T
2. Allowed Freq.: L = n λ , ν = n
, n = 1, 2, 3, . 3. Fundamental/1st harmonics: ν 0 = v
2 2L µ 4L
. .. q 4L
st
3. Fundamental/1 harmonics: ν0 = 1 st rd
4. 1 overtone/3 harmonics: ν1 = 3ν0 = 3v
2L µ
T

5. 2nd overtone/5th harmonics: ν2 = 5ν0 = 5v

S1 P
4L y
6. Only odd harmonics are present. Path difference: ∆x = dy
D d θ
S2
D
A Phase difference: δ = 2π
λ
∆x
N
Open organ pipe: Interference Conditions: for integer n,
L A
N 2nπ, constructive;
δ=
A (2n + 1)π, destructive,
1. Boundary condition: y = 0 at x = 0
Allowed freq.: L = n2λ , ν = n4Lv , n = 1, 2, . . .
1
2. Fundamental/1st harmonics: ν0 = v n+
nλ, λ, destructive
constructive;
2L ∆x = 2
3. 1st overtone/2nd harmonics: ν1 = 2ν0 = 2v
2L
nd rd
4. 2 overtone/3 harmonics: ν2 = 3ν0 = 3v Intensity:
√
I = I1 + I2 + 2 I1I2 cos δ,
2L
√ √ 2 √ 2
5. All harmonics are present. Imax = I1 + I2 , min = — I2

√
I I1
I1 = I2 : I = 4I0 cos2 δ , Imax = 4I0, Imin = 0
2
l1 + d
Fringe width: w = λD
d
l2 + d
Resonance column: Optical path: ∆x′ = µ∆x
Interference of waves transmitted through thin film:

l1 + d = λ
2
, l2 + d = 3λ
4
, v = 2(l2 − l1)ν
nλ, constructive;
∆x = 2µd
Beats: two waves of almost equal frequencies ω 1 ≈ 2 = 2
ω n+ 1
λ, destructive.
p1 = p0 sin ω1(t − x/v), p2 = p0 sin ω2(t − x/v)
p = p1 + p2 = 2p0 cos ∆ω(t − x/v) sin ω(t − x/v) Diffraction from a single slit: θ
y
b
y
ω = (ω1 + ω2)/2, ∆ω = ω1 − ω2 (beats freq.)
D
For Minima: nλ = b sin θ ≈ b(y/D)
Doppler Effect:
v + uo Resolution: sin θ = 1.22λ
b
ν= ν0
v − us θ
Law of Malus: I = cos2 θ I0 I
I0
where, v is the speed of sound in the medium, u0 is
the speed of the observer w.r.t. the medium, consid-
ered positive when it moves towards the source and
negative when it moves away from the source, and us
is the speed of the source w.r.t. the medium, consid-
ered positive when it moves towards the observer and
negative when it moves away from the observer.
2.4 : Light Waves

Visit www.concepts-of-physics.com to buy
Plane Wave: E = E0 sin ω(t −vx ), I = I0 “IIT JEE Physics: Topic-wise Complete Solutions”
and our other books. Written by IITians, Foreword
by Dr. HC Verma, Appreciated by Students.
Spherical Wave: E = aE0
r sin ω(t − vr ), I = I0
r2

Young’s
double slit experiment

h i
3 Optics Lens maker’s formula: 1
= (µ − 1) 1
− 1
f R1 R2
3.1: Reflection of Light f

1
Lens formula: 1
− = 1
, m= v
normal v u f u
Laws of reflection: (i)
incident i r reflected
u v
Incident ray, reflected ray, and normal lie in the same
plane (ii) ∠i = ∠r Power of the lens: P = 1
f
, P in diopter if f in metre.
Two thin lenses separated by distance d:

Plane mirror:
d d
(i) the image and the object are equidistant from mir- 1 1 1 d
= + − d
ror (ii) virtual image of real object F f1 f2 f1f2
f1 f2
I
Spherical Mirror: O
f
v
3.3: Optical Instruments
u
Simple microscope: m = D/f in normal adjustment.
1. Focal length f = R/2
Objective Eyepiece
2. Mirror equation: 1 + 1 = 1
v u f
v O ∞
3. Magnification: m = − u Compound microscope:
u v fe
3.2: Refraction of Light D
Refractive index: µ = speed of light in vacuum

= c 1. Magnification in normal adjustment: m = v D
speed of light in medium v u fe
incident reflected 2. Resolving
θ
power: R = 1
= 2µ sin
Snell’s Law: sin i

= µ2
µ1 i
∆d λ
sin r µ1
µ2 fo fe
r refracted
Apparent depth: µ = real depth

= d
Astronomical telescope:
apparent depth d' d'
d I
O
Critical angle: θc = sin−1 1

µ fo
µ θc 1. In normal adjustment: m = − , L = fo + fe
fe
2. Resolving power: R = 1
= 1
∆θ 1.22λ
A 3.4: Dispersion
δ
Deviation by a prism:
i i'
r r' Cauchy’s equation: µ = µ0 + λA2 , A>0
µ
Dispersion by prism with small A and i:
δ = i + i − A,
′
general result 1. Mean deviation: δy = (µy − 1)A
A+δm
sin ′ 2. Angular dispersion: θ = (µv − µr)A
µ= 2
, i = i for minimum deviation
sin 2A Dispersive power: ω = µv −µr ≈ (if A and i small)
θ
δ µy −1 δy
δm = (µ − 1)A, for small A δm
A µ'
' i
Dispersion without deviation:
i
µ A'
µ1 µ2 (µy − 1)A + (µ y − 1)A = 0
′ ′
Refraction at spherical surface:

P Q Deviation without′ dispersion:
(µ − µ )A = (µ − µ′ )A′
O v

v r v r
µ2 µ1 µ2 − µ1 µ1v
v − u= R , m = µ2u

4 Heat and Thermodynamics 4.4: Theromodynamic Processes
4.1: Heat and Temperature First law of thermodynamics: ∆Q = ∆U + ∆W
Temp. scales: F = 32 + 59 C, K = C + 273.16 Work done by the gas:

Ideal gas equation: pV = nRT , n : number of moles ∫ V2
∆W = p∆V, W= pdV
V1
van der Waals equation: p + Va 2 (V − b) = nRT
V2
Wisothermal = nRT ln
Thermal expansion: L = L0(1 + α∆T ), V1
A = A0(1 + β∆T ), V = V0(1 + γ∆T ), γ = 2β = Wisobaric = p(V2 − V1)
3α
Thermal stress of a material: F
=Y ∆l Wadiabatic = p1V1 − p2V2

A l γ−1
Wisochoric = 0
4.2: Kinetic Theory of Gases
General: M = mNA, k = R/NA T1
Q1
n Efficiency of the heat engine: W
Q2
Maxwell distribution of speed: T2
vp vrms v work done by the engine Q1 − Q2

v¯ η= =
q q heat supplied to it Q1
RMS speed: vrms = 3kT = 3RT
Q T
q
m M ηcarnot =1− 2 =1− 2
Q1 T1
Average speed: v¯ = 8RT
πm q
=q πM
T1
8kT 2kT Coeff. of performance of refrigerator: Q1
Most probable speed: vp = m

W
Q2
T2
Pressure: p = 1
ρv2
3 rms COP = Q2
= Q2
W Q1−Q2
Equipartition of energy: K = 1
kT for each degree of ∫
2 f ∆Q
f
freedom. Thus, K = kT for molecule having f Entropy: ∆S = ∆Q
T
, Sf − S i = i T
2
grees of freedoms. de-
Const. T : ∆S = Q
, Varying T : ∆S = ms ln Tf
T Ti
Internal energy of n moles of an ideal gas is U = f nRT
2
. Adiabatic process: ∆Q = 0, pV γ = constant
4.3: Specific Heat

4.5: Heat Transfer
Specific heat: s = Q
m∆T Conduction: ∆Q
= −KA ∆T
∆t x
Latent heat: L = Q/m
Specific heat at constant volume: C Thermal resistance: R = KA
x
∆Q
=
v n∆T Rseries = R1 + R2 1 x1
+ x2 K1 K2 A
V =
Specific heat at constant pressure: C A K1 K2
∆Q x1 x2
=
p n∆T
p K2 A2
1 1 1
Relation between Cp and Cv: Cp − Cv = R Rparallel = R1 + R2 = 1
x (K1A1 + K2A2) K1 A1
x
Ratio of specific heats: γ = Cp/Cv
Relation between U and C : ∆U = nC ∆T
emissive power E
v v Kirchhoff’s Law: absorptive power =abody
body
= Eblackbody
Specific heat of gas mixture: Eλ
Cv =

n1Cv1 + n2Cv2 n 2 C p2 Wien’s displacement law: λmT = b

n 1 C p1
n1 + n2 , γ= n1Cv1 + λ
+ λm
n2Cv2
Molar internal energy of an ideal gas: U = f

RT Stefan-Boltzmann law: ∆Q
= σeAT 4
2
, ∆t
f = 3 for monatomic and f = 5 for diatomic
gas. Newton’s law of cooling: dT
dt
= −bA(T − T0)

5 Electricity and Magnetism 5.3: Capacitors
5.1: Electrostatics Capacitance: C = q/V

Coulomb’s law: F→ = 1 q1q2
rˆ −q +q
4πє0 r2 q1 r Parallel plate capacitor: C = ϵ0A/d
q2 A A
d
Electric field: E→ (→r) = 1q
E→
q →r
rˆ r2
4πє0 r2
1 q1q2
Electrostatic energy: U = − +q
r1
4πє0r1r2
Spherical capacitor: C =
4πє0 r r2−r1 −q
Electrostatic potential: V = 1 q
4πє0 r
∫ →r
dV = − E→ · →r, V (→r) = E · d→r 2πє05
− Cylindrical capacitor: C = r2
→∞ ln(r2 /r1 ) l
r1
p→
Electric dipole moment: p→ = qd→
−q +q A
d Capacitors in parallel: Ceq = + C2 C1 C2
C1 B
Potential of a dipole: V = 1 p cos 8 V (r)
θr
4πє0 r2
p→ Capacitors in series: 1
= C
1
+ 1
C C1 C2
Ceq 1 2 A B
Er Force between plates of a parallel plate capacitor:

Field of a dipole: θr F= Q
2
Eθ 2Aє0
p→ 2
Er = 1 2p cos 8
, E8 = 1 p sin 8 Energy stored in capacitor: U = 1
CV 2 = Q
= 1
QV
4πє0 4πє0 r3 2 2C 2
r3
→ → Energy density in electric field E: U/V = 1
ϵ0E2
Torque on a dipole placed in E: →τ = p→ × E 2
є0KA
Pot. energy of a dipole placed in E→ : U = −p→ · Capacitor with dielectric: C = d
E→
5.4: Current electricity
5.2: Gauss’s Law and its Applications
H
Electric flux: φ = E→ · d S→
H Current density: j = i/A = σE
Gauss’s law: E→ · d S→ = qin/ϵ0
Drift speed: vd = 1 eE
2 m
i
τ = neA
Field of a uniformly charged ring on its axis:

Resistance of a wire: R = ρl/A, where ρ = 1/σ
1 qx a
EP = 4πє0 q x P
Temp. dependence of resistance: R = R0(1 + α∆T )
(a2+x2)3/2
E→ Ohm’s law: V = iR
E and V (
of a uniformly charged sphere:
1 Qr
, for r < R Kirchhoff’s Laws: (i) The Junction Law: The algebraic
4πє0 R3 E
E 1 Q sum of all the currents directed towards a node is zero
, for r ≥ R
= ( 4πє0 r i.e., Σnode Ii = 0. (ii)The Loop Law: The algebraic
r2 O
Q r
2 R sum of all the potential differences along a closed loop
3− , for r < R
8πє0R V
V= 1 Q
,
R2
for r ≥ R in a circuit is zero i.e., Σ loop∆ i =
4πє0 r O
r V 0. A
R Resistors in parallel: 1 = 1 + 1
R1 R2 R1 R2
E and V of a uniformly charged spherical shell: Req
B
0, for r < ( E
R
4πє0 Q
R 1 Q
V= 1
Q , for r ≥ R
, r
1
4πє0 O
E= r2 for r < R R

V series: Req = R1 + R2 R1 R2
Resistors in A
R1 RB
2
↑ G
4πє0 r
, for r ≥ R r Wheatstone bridge:
O R R3 R4
Field of a line charge: E = λ

2πє0 r
V
Balanced if R1/R2 = R3/R4.
Field of an infinite sheet: E = σ
2є 0
Electric Power: P = V 2/R = I2R = IV
Field in the vicinity of conducting surface: E = σ
є0

i ig G i Energy of a magnetic dipole placed in B→ :

Galvanometer as an Ammeter:
i − ig U = −µ→ · B→
S
igG = (i − ig)S 5
Hall effect: Vw = Bi
ned B→
y x
Galvanometer as a Voltmeter: R G w
↑ i d z
A ig B
VAB = ig(R + G)
5.6: Magnetic Field due to Current
R C
Charging of capacitors: ⊗ B→
Biot-Savart law: d B→ µ0 i d→5
i
= →r × 8
3
→
4π r r
h i V d→5
t
q(t) = CV 1 − e −
RC
82
C
Discharging of capacitors: q(t) = q0e— RC
t
Field due to a straight conductor: i d ⊗ B→
q(t)
81
R
µ 0i
Time constant in RC circuit: τ = RC B= 4πd
(cos θ1 − cos θ2)
µ0i
Field due to an infinite straight wire: B = 2πd
Peltier effect: emf e = ∆H

= Peltier heat
.
dF µ i i i1 i2
∆Q charge transferred Force between parallel wires: d5

= 0 1 2
2πd
Seeback effect: e d
T
T0 Tn Ti a
P
1. Thermo-emf: e = aT + bT 1 2
d
Field on the axis of a ring: i B→
2. Thermoelectric power: 2de/dt = a + bT
.
2
µ0ia
3. Neutral temp.: Tn = −a/b. BP = 2(a2+d2)3/2
4. Inversion temp.: Ti = −2a/b.
a
∆H Thomson heat µ0i8
Field at the centre of an arc: B = B→ 8 i
Thomson effect: emf e = = = σ∆T . 4πa ⊙
∆Q charge transferred a
Faraday’s law of electrolysis: The mass deposited is

µ0i
Field at the centre of a ring: B = 2a
m = Zit = 1
F
Eit H
Ampere’s law: B→ · d→l = µ0Iin
where i is current, t is time, Z is electrochemical equiv-
alent, E is chemical equivalent, and F = 96485 C/g
is Faraday constant. Field inside a solenoid: B = µ0ni, n = N
5
5
Ni
5.5: Magnetism Field inside a toroid: B = µ2πr
0
r
Lorentz force on a moving charge: F→ = q→v × B→ +

qE→ B→
Field of a bar magnet: 2
Charged particle in a uniform magnetic field: B→ 1

S dd
v N
q mv 2πm
r= qB , T = qB
r µ0 2M µ0 M
B→ ⊗ B1 = 4π d3 , B2 = 4π d3
Force on a current carrying wire: δ

Angle of dip: Bh = B cos

Formulae Sheet for Physics B
www.concepts- of-physics.com | δpg. 19
→ →
Horizontal Bh Bv B
5
F i
F → = i →l × →
µ0ni
Tangent galvanometer: Bh tan θ = , i = K tan θ
B→
2r
Magnetic moment of a current loop (dipole):
Moving coil galvanometer: niAB = kθ, i = k
θ
µ→
A→
µ→ = i A→ nAB
i q
Time period of magnetometer: T = 2π MBIh
Torque on a magnetic dipole placed in B→ : →τ = µ→ × B→

Permeability: → →
B = µH

5.7: Electromagnetic Induction C R Z

1
H RC circuit: i ωC
φ
Magnetic flux: φ = B→ ·
dS→
e0 s˜ in
R
dφ
√
Faraday’s law: e = − Z = R 2 + (1/ωC) 2 , tan φ = 1
dt ωCR
Lenz’s Law: Induced current create a B-field that op- L R R
poses the change in magnetic flux.
LR circuit: i
ωL
φ
√
e0 s˜ in
Z
+
Motional emf: e = Blv Z= R2 + ω2L2, tan φ = ωL
R
5 →v
⊗ B→
—
L C R 1 1
Z
Self inductance: φ = Li, e = −L di
LCR Circuit: i
ωC
ωC − ωL
φ
˜
ωL
dt q e0 s i n ωt R
2 2 1 2 −ωL
Z= R 2+ q − ωL , tan φ = 1
Self inductance of a solenoid: L = µ0n (πr
h i ωC
ωC R
l) t 1 1
Growth of current in LR circuit: i = e
1 − e− L/R
νresonance =
R 2π LC
i
L Power factor: P = ermsirms cos φ
R
0.63 R
e
e N1 N2
˜ ˜
e1 e2
L
t Transformer: NN21 = e1
e2 , e1i1 = e2i2
S i R
i1 i2
t
Decay of current in LR circuit: i = i0e— L/R √
Speed of the EM waves in vacuum: c = 1/ µ0ϵ0
L i
R
i0
0.37i0
t
S i L
R
Time constant of LR circuit: τ = L/R
Energy stored in an inductor: U = 12 Li2

2
Energy density of B field: u = U
= B
V 2µ0
Mutual inductance: φ = Mi, e = −M didt
EMF induced in a rotating coil: e = NABω sin ωt

i
Alternating current: t
T
i = i0 sin(ωt + φ), T = 2π/ω
∫
T
Average current in AC: ¯i = T1 0 i dt =
0 i1/2
h i2
RMS current: irms = 1T 0
i2T
= i0
√
t
2
dt T
Energy: E = irms2RT Visit www.concepts-of-physics.com to buy

Capacitive reactance: Xc = 1
“IIT JEE Physics: Topic-wise Complete Solutions”
ωC
and our other books. Written by IITians, Foreword
Inductive reactance: XL = ωL by Dr. HC Verma, Appreciated by Students.
Imepedance: Z = e0/i0

6 Modern Physics N
N0
6.1: Photo-electric effect Population at time t: N = N0e−λt N0

2
Photon’s energy: E = hν = hc/λ O t1/2 t
Photon’s momentum: p = h/λ = E/c Half life: t1/2 = 0.693/λ

Max. KE of ejected photo-electron: Kmax = hν − φ Average life: tav = 1/λ
Threshold freq. in photo-electric effect: ν0 = φ/h

Population after n half lives: N = N0/2n.
V0
Mass defect: ∆m = [Zmp + (A − Z)mn] − M
Stopping potential: Vo = hc
e 1
λ —φ
e
hc
e
Binding energy: B = + (A − Z)mn — M ] 2
φ 1
hc
λ [Zmp c
—φe
Q-value: Q = U − U
i f
de Broglie wavelength: λ =
h/p Energy released in nuclear reaction: ∆E = ∆mc2
where ∆m = mreactants − mproducts.
6.2: The Atom
Energy in nth Bohr’s orbit: 6.4: Vacuum tubes and Semiconductors
mZ2e4 13.6Z2 D
En = − , En = − eV Half Wave Rectifier:
8ϵ 02h2n2 n2 R Output
Radius of the nth Bohr’s orbit: ˜

ϵ0h2n2
n2a0 ˚ Full Wave Rectifier:
rn =
πmZe 2
, rn =
Z
, a0 = 0.529 A ˜ Output
Quantization of the angular momentum: l = nh

Grid
2π
Photon energy in state transition: E2 − E1 = hν Triode Valve: Cathode
Filament Plate
E2 E2
hν hν ∆Vp
E1
Emission
E1 Plate resistance of a triode: rp = ∆ip
Absorption ∆Vg =0
Wavelength of emitted radiation: for a transition

Transconductance of a triode: g = ∆ip
from nth to mth state: m g ∆Vp=0
∆V
∆Vgp
1 12 1 Amplification by a triode: µ = − ∆V ∆ip=0
λ = RZ2 n − m2
Relation between rp, µ, and gm: µ = rp × gm
I Kα
X-ray spectrum: λmin = hc

eV Kβ Ie Ic
Current in a transistor: Ie = Ib + Ic
λmin λα λ
Ib
√
Moseley’s law: ν = a(Z − b) I
X-ray diffraction: 2d sin θ = nλ α and β parameters of a transistor: α = Ie

c
, β =
Ic α
Ib
, β = 1−α
Heisenberg uncertainity principle: Nuclear radius: R = R0A1/3, R0 ≈ 1.1 × 10−15 m
∆p∆x ≥ h/(2π), ∆E∆t ≥ h/(2π)
dt
Decay rate: dN
= −λN
6.3: The Nucleus

Transconductance: gm = ∆Ic
∆V
be
Logic Gates:
AND OR NAND NOR XOR
A B AB A+B AB A+B AB¯ +
0 0 0 0 1 1 A¯ B
0
0 1 0 1 1 0 1
1 0 0 1 1 0 1
1 1 1 1 0 0 0


Physics Formulas

Uploaded by

Copyright:

Available Formats

Physics Formulas

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Physics Formulas

Uploaded by

Copyright:

Available Formats

Formulae Sheet for Physics www.concepts- of-physics.com | pg.

Physics formulas from Mechanics, Waves, Optics, Heat and

0.1: Physical Constants Relative Velocity: →vA/B = →vA − →vB

Speed of light c 3 × 108 m/s

1 MECHANICS Pseudo force: pseudo

Dot product: →a ·→b = axbx + ayby + azbz = ab cos θ g

|→a × →b| = ab sin θ

→vav = ∆→r/∆t, →vinst = d→r/dt

Get Formulas www.concepts-of-physics.com Get Our Book

Potential energy: F = −∂U/∂x for conservative

Ugravitational = mgh, Uspring = 1 kx2 2

Work done by conservative forces is path

Get Formulas www.concepts-of-physics.com Get Our Book

Mechanical energy: E = U + K. Conserved if forces are

ω = ω0 + αt, θ = ωt + 21 αt2, ω2 − ω02 = 2αθ

CM of few useful configurations: ring disk shell sphere rod hollow

Get Formulas www.concepts-of-physics.com Get Our Book

If v2 = 0 and m1 m2 then v1′ = −v1. Variation of g with height: goutside ≈ g 1 − 2h

1.6: Rigid Body Dynamics Effect of earth rotation on apparent weight:

Angular Accel.: αav = ∆ω

Get Formulas www.concepts-of-physics.com Get Our Book

x1 = A1 sin ωt, x2 = A2 sin(ωt +

First: Elliptical orbit with sun at one of the ∆l/l ∆V Aθ

1.8: Simple Harmonic Motion

√ Surface tension: S = F/l

Capillary rise: h = 2S cos θ

Hydrostatic pressure: p = ρgh

Total energy: E = U + K = 1 Equation of continuity: A1v1 = A2v2 v2

Get Formulas www.concepts-of-physics.com Get Our Book

Get Formulas www.concepts-of-physics.com Get Our Book

2 Waves 4. 1st overtone/2nd harmonics: ν1 = 2

2.1 : Waves Motion 5. 2nd overtone/3rd harmonics: ν2 = 3

Get Formulas www.concepts-of-physics.com Get Our Book

Notation: Amplitude A, Frequency ν, Wavelength λ, Pe-

Progressive wave travelling with speed v: λ/2

y = f (t − x/v), ~ +x; y = f (t + x/v), ~ 1. Boundary conditions: y = 0 at x = 0

Interference: 2.3 : Sound Waves

y1 = A1 sin(kx − ωt), y2 = A2 sin(kx − ωt + δ) Displacement wave: s = s0 sin ω(t − x/v)

y = y1 + y2 = A sin(kx − ωt + ϵ) Pressure wave: p = p0 cos ω(t − x/v), p0 = (Bω/v)s0

String fixed at both ends:

λ/2 1. Boundary condition: y = 0 at x = 0

Get Formulas www.concepts-of-physics.com Get Our Book

Get Formulas www.concepts-of-physics.com Get Our Book

5. 2nd overtone/5th harmonics: ν2 = 5ν0 = 5v

5. All harmonics are present. Imax = I1 + I2 , min = — I2

Resonance column: Optical path: ∆x′ = µ∆x

Interference of waves transmitted through thin film:

2.4 : Light Waves

Get Formulas www.concepts-of-physics.com Get Our Book

double slit experiment

Get Formulas www.concepts-of-physics.com Get Our Book

3.1: Reflection of Light f

Two thin lenses separated by distance d:

Refractive index: µ = speed of light in vacuum

Snell’s Law: sin i

Apparent depth: µ = real depth

Critical angle: θc = sin−1 1

Refraction at spherical surface:

Get Formulas www.concepts-of-physics.com Get Our Book