CLASS 12 : PHYSICS
FORMULA
BOOK
ELECTRIC CHARGES AND FIELDS 1 q
(ii) At very large distance i.e. r >> a E =
4 πε 0 r 2
k q1q2 1 q1q2
Coulomb’s law : F = =
r 2 4 πε r 2 Torque on an electric dipole placed in a uniform
Relative permittivity or dielectric constant : electric field : τ = p × E or τ = pE sin θ
ε Potential energy of an electric dipole in a
i.e., ε r or K =
ε0 uniform electric field is U = –pE(cosq2 – cosq1)
Electric field intensity at a point distant r from where q1 & q1 are initial angle and final angle
1 q
a point charge q is E = . between
4 πε 0 r 2
Electric dipole momentm, Electric flux φ = E ⋅ dS
Electric field intensity on axial line (end on Gauss’s law :
position) of the electric dipole
Electric field due to thin infinitely long straight
(i) At the point r from the centre of the electric
wire of uniform linear charge density l
1 2 pr
dipole, E = . λ
4 πε 0 (r 2 − a 2 )2 E= ,
2 πε 0r
(ii) At very large distance i.e., (r > > a), (i) At a point outside the shell i.e., r > R
2p
E= 1 q
4 πε 0r 3 E=
4 πε 0 r 2
Electric field intensity on equatorial line (board (ii) At a point on the shell i.e., r = R
on position) of electric dipole
1 q
E=
(i) At the point at a distance r from the centre 4 πε 0 R 2
1 p (iii) At a point inside the shell i.e., r < R
of electric dipole, E = .
4 πε 0 (r 2 + a 2 )
E=0
(ii) At very large distance i.e., r > > a, Electric field due to a non conducting solid
1 p
sphere of uniform volume charge density r
E= . and radius R at a point distant r from the centre
4 πε 0 r 3
of the sphere is given as follows :
Electric field intensity at any point due to an (i) At a point outside the sphere i.e., r > R
1 p 1 q
electric dipole E = 1 + 3 cos 2 θ E= ·
4 πε 0 r 3 4 πε 0 r 2
Electric field intensity due to a charged ring (ii) At a point on the surface of the sphere
(i) At a point on its axis at distance r from its i.e., r = R
1 q
1 qr E= ·
centre, E = 4 πε 0 R 2
4 πε 0 (r + a 2 )
2
Physics 1
, (iii) At a point inside the sphere i.e., r < R
Relationship between E and V
ρr 1 q r
E= = · , for r < R E = −∇V
3ε 0 4 πε 0 R 3
Electric field due to a thin non conducting where
infinite sheet of charge with uniformly charge
surface density s is E =
σ Electric potential energy of a system of two
2ε0 1 q1q2
point charges is U =
Electric field between two infinite thin plane 4 πε 0 r12
parallel sheets of uniform surface charge Capacitance of a spherical conductor of radius
density s and – s is E = s/e0. R is C = 4pe0R
ELECTROSTATIC POTENTIAL AND Capacitance of an air filled parallel plate
CAPACITANCE capacitor
W Capacitance of an air filled spherical capacitor
Electric potential V =
q
ab
Electric potential at a point distant r from a C = 4 πε 0
b−a
point charge q is V = q
4 πε 0r
Capacitance of an air filled cylindrical capacitor
The electric potential at point due to an electric 2 πε 0 L
C=
dipole b
ln
1 p cos θ a
V=
4 πε 0 r 2 Capacitance of a parallel plate capacitor
Electric potential due to a uniformly charged with a dielectric slab of dielectric constant K,
spherical shell of uniform surface charge completely filled between the plates of the
density s and radius R at a distance r from the
capacitor, is given by
centre the shell is given as follows :
(i) At a point outside the shell i.e., r > R When a dielectric slab of thickness t and
1 q dielectric constant K is introduced between the
V=
4 πε 0 r plates, then the capacitance of a parallel plate
(ii) At a point on the shell i.e., r = R ε0 A
1 q capacitor is given by C =
V= 1
4 πε 0 R d − t 1 −
K
(iii) At a point inside the shell i.e., r > R
1 q When a metallic conductor of thickness t is
V= introduced between the plates, then capacitance
4 πε 0 R
Electric potential due to a non-conducting solid of a parallel plate capacitor is given by
sphere of uniform volume charge density r and
radius R distant r from the sphere is given as
follows : Energy stored in a capacitor :
(i) At a point outside the sphere i.e. r > R 1 1 1 Q2
1 q U= CV 2 = QV =
V= 2 2 2 C
4 πε0 r 1
Energy density : u = ε 0E 2
(ii) At a point on the sphere i.e., r = R 2
1 q
V= 1 1 1 1
4 πε 0 R Capacitors in series : = + + .... +
CS C1 C2 Cn
(iii) At a point inside the sphere i.e., r < R
1 q( 3R 2 − r 2 ) Capacitors in parallel : CP = C1 + C2 + .... + Cn
V=
4 πε 0 2R3
2 Physics
FORMULA
BOOK
ELECTRIC CHARGES AND FIELDS 1 q
(ii) At very large distance i.e. r >> a E =
4 πε 0 r 2
k q1q2 1 q1q2
Coulomb’s law : F = =
r 2 4 πε r 2 Torque on an electric dipole placed in a uniform
Relative permittivity or dielectric constant : electric field : τ = p × E or τ = pE sin θ
ε Potential energy of an electric dipole in a
i.e., ε r or K =
ε0 uniform electric field is U = –pE(cosq2 – cosq1)
Electric field intensity at a point distant r from where q1 & q1 are initial angle and final angle
1 q
a point charge q is E = . between
4 πε 0 r 2
Electric dipole momentm, Electric flux φ = E ⋅ dS
Electric field intensity on axial line (end on Gauss’s law :
position) of the electric dipole
Electric field due to thin infinitely long straight
(i) At the point r from the centre of the electric
wire of uniform linear charge density l
1 2 pr
dipole, E = . λ
4 πε 0 (r 2 − a 2 )2 E= ,
2 πε 0r
(ii) At very large distance i.e., (r > > a), (i) At a point outside the shell i.e., r > R
2p
E= 1 q
4 πε 0r 3 E=
4 πε 0 r 2
Electric field intensity on equatorial line (board (ii) At a point on the shell i.e., r = R
on position) of electric dipole
1 q
E=
(i) At the point at a distance r from the centre 4 πε 0 R 2
1 p (iii) At a point inside the shell i.e., r < R
of electric dipole, E = .
4 πε 0 (r 2 + a 2 )
E=0
(ii) At very large distance i.e., r > > a, Electric field due to a non conducting solid
1 p
sphere of uniform volume charge density r
E= . and radius R at a point distant r from the centre
4 πε 0 r 3
of the sphere is given as follows :
Electric field intensity at any point due to an (i) At a point outside the sphere i.e., r > R
1 p 1 q
electric dipole E = 1 + 3 cos 2 θ E= ·
4 πε 0 r 3 4 πε 0 r 2
Electric field intensity due to a charged ring (ii) At a point on the surface of the sphere
(i) At a point on its axis at distance r from its i.e., r = R
1 q
1 qr E= ·
centre, E = 4 πε 0 R 2
4 πε 0 (r + a 2 )
2
Physics 1
, (iii) At a point inside the sphere i.e., r < R
Relationship between E and V
ρr 1 q r
E= = · , for r < R E = −∇V
3ε 0 4 πε 0 R 3
Electric field due to a thin non conducting where
infinite sheet of charge with uniformly charge
surface density s is E =
σ Electric potential energy of a system of two
2ε0 1 q1q2
point charges is U =
Electric field between two infinite thin plane 4 πε 0 r12
parallel sheets of uniform surface charge Capacitance of a spherical conductor of radius
density s and – s is E = s/e0. R is C = 4pe0R
ELECTROSTATIC POTENTIAL AND Capacitance of an air filled parallel plate
CAPACITANCE capacitor
W Capacitance of an air filled spherical capacitor
Electric potential V =
q
ab
Electric potential at a point distant r from a C = 4 πε 0
b−a
point charge q is V = q
4 πε 0r
Capacitance of an air filled cylindrical capacitor
The electric potential at point due to an electric 2 πε 0 L
C=
dipole b
ln
1 p cos θ a
V=
4 πε 0 r 2 Capacitance of a parallel plate capacitor
Electric potential due to a uniformly charged with a dielectric slab of dielectric constant K,
spherical shell of uniform surface charge completely filled between the plates of the
density s and radius R at a distance r from the
capacitor, is given by
centre the shell is given as follows :
(i) At a point outside the shell i.e., r > R When a dielectric slab of thickness t and
1 q dielectric constant K is introduced between the
V=
4 πε 0 r plates, then the capacitance of a parallel plate
(ii) At a point on the shell i.e., r = R ε0 A
1 q capacitor is given by C =
V= 1
4 πε 0 R d − t 1 −
K
(iii) At a point inside the shell i.e., r > R
1 q When a metallic conductor of thickness t is
V= introduced between the plates, then capacitance
4 πε 0 R
Electric potential due to a non-conducting solid of a parallel plate capacitor is given by
sphere of uniform volume charge density r and
radius R distant r from the sphere is given as
follows : Energy stored in a capacitor :
(i) At a point outside the sphere i.e. r > R 1 1 1 Q2
1 q U= CV 2 = QV =
V= 2 2 2 C
4 πε0 r 1
Energy density : u = ε 0E 2
(ii) At a point on the sphere i.e., r = R 2
1 q
V= 1 1 1 1
4 πε 0 R Capacitors in series : = + + .... +
CS C1 C2 Cn
(iii) At a point inside the sphere i.e., r < R
1 q( 3R 2 − r 2 ) Capacitors in parallel : CP = C1 + C2 + .... + Cn
V=
4 πε 0 2R3
2 Physics
