CP: Electrostatics February 1, 2010. Electrostatics – Chap. 32.
Electrostatics
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ELECTROSTATICS 1. Quantization of Charge: Any charged body, big or small, has a total charge q which is an integral multiple of e, i.e. q = ± ne, where n is an integer having values 1, 2, 3, … etc, ‘e’ is the charge of electron which is equal to 1.6 × 10 –19 C. 2. Coulomb’s law: 1 2 2 1 qq ˆ F r 4 r = ⋅ πε 3. Electric Field: 0 F E q = , where q 0 is the unit positive charge. Electric field is also equal to Electric flux (φ) per unit normal area. E A φ = . Field due to a point charge: 2 0 q 1 E 4 r = πε 4. Electric Potential: Electric potential due to a number of point charges n i i1 0 i 1 q V 4 r = = πε ∑ Potential Difference: 2 1 r 2 1 r V V E dr - =- ⋅ ∫ ⇒ dV E dr =- The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy: Electric potential energy between two point charges 1 2 0 qq U 4 r = πε 6. Electric Dipole Moment: Two point charges of equal magnitude but opposite signs separated by a small distance form an electric dipole. Dipole moment is vector quantity, p q 2l = × . 7. Torque on a Dipole in an Electric field: Torque = 2q sin E θ× In vector form: Torque = p E × Potential Energy of a Dipole in an Electric Field: U pE =- ⋅ No electric field can exist inside a conducting material. Force on a dipole: E E F p where r r ∂ ∂ = ∂ ∂ is the derivative of electric field with respect to distance along the direction of the dipole. Gauss’ Theorem: 0 q E dA ⋅ = ε ∫ , where q is equal to the net charge enclosed with the surface. Gauss law for Gravitation: g dA 4 GM ⋅ =- π ∫ , where M is the total mass enclosed within the closed surface. 7. Capacitance: Capacitor is a device for storing charge. Mathematically, Q = CV, the unit of C in farad. For parallel plate capacitor: 0 A C d ε = , where A = Plate area, d = Distance between the plates
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Transcript of Electrostatics
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ELECTROSTATICS
1. Quantization of Charge: Any charged body, big or small, has a total charge q which is an integralmultiple of e, i.e. q = ne, where n is an integer having values 1, 2, 3, etc, e is the charge ofelectron which is equal to 1.6 1019 C.
2. Coulombs law: 1 221 q q
F r4 r
=
pi
3. Electric Field:0
FEq
=
, where q0 is the unit positive charge.
Electric field is also equal to Electric flux () per unit normal area. EA
=
.
Field due to a point charge: 20
q 1E4 r
=
pi
4. Electric Potential:
Electric potential due to a number of point chargesn
i
i 10 i
1 qV4 r
=
=
pi
Potential Difference:2
1
r
2 1r
V V E dr =
dVEdr
=
The electric field is along the direction where the potential decreases at the maximum rate.5. Electric Potential Energy:
Electric potential energy between two point charges 1 20
q qU4 r
=
pi
6. Electric Dipole Moment:Two point charges of equal magnitude but opposite signs separated by a small distance form an electricdipole.Dipole moment is vector quantity, p q 2l= .
7. Torque on a Dipole in an Electric field:Torque = 2q sin EIn vector form: Torque = p E
Potential Energy of a Dipole in an Electric Field:U p E=
No electric field can exist inside a conducting material.
Force on a dipole: E EF p wherer r
=
is the derivative of electric field with respect to distance along
the direction of the dipole.
Gauss Theorem:0
qE dA =
, where q is equal to the net charge enclosed with the surface.
Gauss law for Gravitation: g dA 4 GM = pi
, where M is the total mass enclosed within the closedsurface.
7. Capacitance:Capacitor is a device for storing charge. Mathematically, Q = CV, the unit of C in farad.For parallel plate capacitor: 0AC
d
= , where A = Plate area, d = Distance between the plates
-
8. Energy Stored in a Capacitor:2
2Q 1 1U CV QV2C 2 2
= = =
9. Energy Stored per Unit Volume in an Electric Field (E): 20U 1 E
Volume 2= .
10. Electrostatic Pressure:2
0P
2
=
, where is surface charge density.
11. Electric field and potential for typical situations:
S.No. System Electric field intensity Potential1. Isolated charge
20
1 qE .4 r
=
pi 0
qV4 r
=
pi
Dipole|| 3
0
30
1 2pE .4 x
1 pE .4 y
=
pi
=
pi
|| 20
1V4 x
V 0
=
pi
=
2.
x, y >> a2
30
1 p 3cos 1E4 r
+=
pi2
0
pcosV4 r
=
pi
3. A ring of charge
2 2 3 / 20
1 qxE .4 (R x )= pi + 2 20
1 qV4 R x
=
pi +
4. A disc of charge2 20
xE 12 x R
= +
where is surface chargedensity.
2 2
0V [ R x x]
2
= +
5. Infinite sheet of charge
0E
2
=
---
6. Infinitely long line ofcharge
=
pi0
1 2E4 r
where is
linear charge density.---
7. Finite line of charge
0E (sin sin )
4 x
= + pi
||0
E (cos cos )4 x
=
pi0
sec tanV ln4 sec tan
+ =
pi
EIsolated charge
rq p
y
E
E||q +
2ax
rP
x
px
qR
+
++
++
+
+
++
++
+
+
+
++
++
+
+
++
++
+
+
px
qR
+ + +
+ + ++
+
p++++
r
P
x++++
-
8. Charged spherical shella) Inside, 0 r R, E = 0b) Outside, r R, E = 2
0
q4 rpi
a) Inside, 0 r R,V=0
q4 Rpi
b) Outside, r R, V=0
q4 rpi
9. Solid sphere of chargea) Inside, 0 r R, E=
0
r
3
b) Outside, rR, E=2
0
R R3 r
volume charge density.
a) Inside,0 r R, V=
2 2
20
R r36 R
b) Outside,r R, V =
3
0
R 13 r
Note : With proper modifications the above formulae can be applied in Gravitation also.
(Like q M,0
14pi
G).
Potential at the edge of a disc0
RV =pi
.
Sel energy of a charged conducting shell:2
0
1 qU8 R
=
pi
Self energy of the uniformly charged sphere (non-conductor) :2
0
3 qU20 R
=
pi
Capacitance and Capacitor:
1. Parallel plate capacitor: If t is the thickness of the dielectric plate between the plates, then0AC
t(d t)k
=
+
Force between the plates of capacitor2
0
qF A2
=
.
2. Spherical capacitor:
0abC 4
b a= pi
, when outer shell is earthed.
2
0bC 4
b a= pi
, when inner shell is earthed.
3. Cylindrical capacitor: 02Cnb / api
=
4. Charging of a capacitor through resistor:Charge t /0q q (1 e ) = Current t /0i i e
= where q0 = C and = CR.
Potential t /V (1 e ) = Energy t / 20U U (1 e ) =
5. Discharging of a capacitor:Charge t /0q q e
=
R
++
++
+
++ + +
++
+
++
R+
++
+
+
+
++ +
-
Current t /0i i e
=
Potential t /V e = Energy 2t /0U U e
=
