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ZIET BHUBANESWAR|
50
3-DAY WORKSHOP ON IMPROVEMENT OF RESULTS FOR CLASS XII, ZIET BHUBANESWAR
IMPORTANT FORMULAE1. ELECTROSTATICS1.Electrostatic force between two charges
= . = .
For air,
=
Fair =
. = ×
2.Electric field intensity due to a point charge,
=
→
→
3.
Electric field intensity due to infinite linear charge density (λ)
= .
4.Electric field intensity near an infinite thin sheet of surface chargedensity
=
For thick sheet
=
.5.Electric potential,
=
→
Electric potential due to a point charge,
= .
6.Relation between electric field and potential
= − =
(numerically)7.Dipole moment,
= . ⃗
8.Torque on a dipole in uniform electric field,
= ×
.9.Potential energy of dipole,
∪= − . = −
10.Work done in rotating the dipole in uniform electric field from orientation Q
1
to Q
2
is
= − = ( − )
11.Electricfield due to a short dipole(i)at axial point,
= .
(ii)at equatorial point,
= .
12.Electric potential due to a short dipole(i)At axial point,
= .
(ii)At equatorial point,
=
.13.Dielectric constant,
= =
14.Capacitance of parallel plate capacitor
ZIET BHUBANESWAR|
51
3-DAY WORKSHOP ON IMPROVEMENT OF RESULTS FOR CLASS XII, ZIET BHUBANESWAR
(i)
=
, in medium of dielectric constant K(ii)
=
( )
; if space between plate partially filled with dielectric of thickness t.15.Combination of capacitors :-(i)In series,
= + +
,
= = , = + +
(ii)In parallel, C
= + + , = + + , = = =
16.Energy stored by capacitor
∪= = =
17.Electrostatic energy density
=
, in air
=
, in medium18.Total electric flux,
= ∮ . = ×
2. Current Electricity
1. Electric current =or I ==2. In case of an electron revolving in a circle of radius r with speed v, period of revolution isT =; Frequency of revolution, v ==,Current, I = ev =
3. Ohm’s law, R =
or V = IR4. Current in terms of drift velocity () is I =enA5. Resistance of a uniform conductor, R ==6. Resistivity or specific resistance,==7. Conductance =8. Conductivity =
or σ =
=9. Current density =or j == en10. Relation between current density and electric field,
j = σ E or E =
j
ZIET BHUBANESWAR|
52
3-DAY WORKSHOP ON IMPROVEMENT OF RESULTS FOR CLASS XII, ZIET BHUBANESWAR
11. Mobility µ =
12. Temperature coefficient of resistance, α =
( )
13. The equivalent resistanceof a number of resistances connected in series is given by=++
+ …..
14. The equivalent resistanceof a number of resistances connected in parallel is given by=
+ + + ….
15. EMF of a cell, E =16. For a cell of internal resistance r, the emf is E = V + Ir = I (R + r)17. Terminal p.d of a cell, V = IR =18. Terminal p.d. when a current is being drawn from the cell, V = E
–
Ir19. Terminal p.d. when the cell is being charged, V = E + Ir20. Internal resistance of a cell, r = R []21. For n cell in series, I =22. For n cells in parallel, I =23. Heat produced by electric current, H =Rt joule =
.
cal24. Electric power, P == VI =R =25. Electric energy, W = Pt = VIt =Rt26. Potential gradient of the potentiometer wire, k =27. For comparing e.m.f.s of two cells,=28. For measuring internal resistance of a cell, r =x R29. For a balanced Wheatstone bridge,=, If X is the unknown resistance=or X =
ZIET BHUBANESWAR|
53
3-DAY WORKSHOP ON IMPROVEMENT OF RESULTS FOR CLASS XII, ZIET BHUBANESWAR
30. in a slide wire bridge, if balance point is obtained at l cm from the zero end,then==
( )
3. Magnetic effect of current
Biot-Savart law (Magnetic field due to current element)
20
sin4
r dl I dB
θπµ
Force acting on a charge moving in a magnetic field
F = qvB
sinor
F
= q(
Bv
)
Magnetic field on the axis of a circular current loop
.)(2
232220
ar a I N B
µ
Magnetic field due to an infinitely long straight current carrying wire
r I B
πµ
2
0
Magnetic field at a point on the axis of a solenoid
nI B
0
µ
Motion of a charged particle in a uniform magnetic field
r
=
qBmvqBmT
π
2
Torque on a rectangular coil in a uniform magnetic field
τ
=
NIBA
sin
Force per unit length acting on each of the two straight parallel metallic conductorscarrying current
r I I lF f
πµ
2
2102
Deflection in moving coil galvanometer

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