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General Values and Vectors by S.S. Education, Kota |
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ELECTRIC CHARGES AND FIELDS S.S. Education, Kota |
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ELECTRIC CHARGES AND FIELDS
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1 Coulomb's Law: [Newtons N]
where: F = force on one charge by
the other[N]
k = 8.99 × 109 [N·m2/C2]
q1 = charge [C]
q2 = charge [C]
r = distance [m]
2 Electric Field: [Newtons/Coulomb or Volts/Meter]
where: E = electric field [N/C or V/m]
k = 8.99 × 109 [N·m2/C2]
q = charge [C]
r = distance [m]
F = force
Electric field lines radiate outward from
positive charges. The electric field
is zero inside a conductor.
3 Relationship of k to Î0:
where: k = 8.99 × 109 [N·m2/C2]
Î0 = permittivity of free space
8.85 × 10-12 [C2/N·m2]
4 Electric Field due to an Infinite Line of Charge: [N/C]
E = electric field [N/C]
l = charge per unit length [C/m}
Î0 = permittivity of free space
8.85 × 10-12 [C2/N·m2]
r = distance [m]
k = 8.99 × 109 [N·m2/C2]
5 Electric Field due to ring of Charge: [N/C]
E = electric field [N/C]
k = 8.99 × 109 [N·m2/C2]
q = charge [C]
z = distance to the charge [m]
R = radius of the ring [m]
6 Electric Field due to a disk Charge: [N/C]
E = electric field [N/C]
s = charge per unit area
[C/m2}
Î0 = 8.85 × 10-12 [C2/N·m2]
z = distance to charge [m]
R = radius of the ring [m]
7 Electric Field due to an infinite sheet: [N/C]
E = electric field [N/C]
s = charge per unit area [C/m2}
Î0 = 8.85 × 10-12 [C2/N·m2]
8 Electric Field inside a spherical shell: [N/C]
E = (kqr/R3)
E = electric field [N/C]
q = charge [C]
r = distance from center of sphere to
the charge [m]
R = radius of the sphere [m]
9 Electric Field outside a spherical shell: [N/C]
E=(kq/r2)
E = electric field [N/C]
q = charge [C]
r = distance from center of sphere to
the charge [m]
10 Average Power per unit area of an electric or magnetic field:
W = watts
Em = max. electric field [N/C]
m0 = 4p × 10-7
c = 2.99792 × 108 [m/s]
Bm = max. magnetic field [T]
A positive charge moving in the same direction as the electric
field direction loses potential energy since the potential of
the electric field diminishes in this direction.
Equipotential lines cross EF lines at right angles.
11 Electric Dipole: Two charges of equal magnitude and
opposite polarity separated by a distance d.
E = electric field [N/C]
k = 8.99 × 109 [N·m2/C2]
Î0 = permittivity of free space 8.85 ×
10-12 C2/N·m2
p = qd [C·m] "electric dipole moment" in the direction negative to positive
z = distance [m] from the dipole center to the point along the dipole axis where the electric field is to be measured
12 Deflection of a Particle in an Electric Field:
2ymv2 = qEL2
y = deflection [m]
m = mass of the particle [kg]
d = plate separation [m]
v = speed [m/s]
q = charge [C]
E = electric field [N/C or V/m
L = length of plates [m]
13 Potential Difference between two Points: [volts V]
&# V = VB- VA = (Δ PE / q) = - Ed
ΔPE = work to move a charge
from A to B [N·m or J]
q = charge [C]
VB = potential at B [V]
VA = potential at A [V]
E = electric field [N/C or V/m
d = plate separation [m]
14 Electric Potential due to a Point Charge: [volts V]
V= k(q/r)
V = potential [volts V]
k = 8.99 × 109 [N·m2/C2]
q = charge [C]
r = distance [m]
15 Potential Energy of a Pair of Charges: [J, N·m or C·V]
PE = q2 V1 k =( (q1q2) /r)
V1 is the electric potential due to q1 at a point P
Q2V1 is the work required to bring q2 from infinity to point P
16 Work and Potential:
ΔU = Uf - Ui - W
U = -W¥
W = F × d = Fd cosq
W qi∫f E. ds
&# 916;V = Vf - Vi = -(W/q)
V=-i∫fE. ds
U = electric potential energy [J]
W = work done on a particle by a field [J]
W¥ = work done on a particle brought from infinity (zero potential) to its present location [J]
F = is the force vector [N]
d = is the distance vector over which the force is applied[m]
F = is the force scalar [N]
d = is the distance scalar [m]
q = is the angle between the force and distance vectors
ds = differential displacement of the charge [m]
V = volts [V]
q = charge [C]
Flux: the rate of flow (of an electric field) [N·m2/C]
j E dA
= ∫ E(cosq )dA
j is the rate of flow of an electric field [N·m2/C]
&# 8747; integral over a closed surface
E is the electric field vector [N/C]
A is the area vector [m2] pointing
outward normal to the surface.
17 Gauss' Law:
Î0 = j qenc
Î0 ∫E. E dA= qenc
Î0 = 8.85 × 10-12 [C2/N·m2]
j is the rate of flow of an electric
field [N·m2/C]
qenc = charge within the gaussian
surface [C]
&# 8747; integral over a closed surface
E is the electric field vector [J]
A is the area vector [m2] pointing
outward normal to the surface.
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