Electrostatics Flashcards
(131 cards)
1
Q
What is Coulomb’s law?
A
F2 = F1 = (Q1Q2)/(4pipermitivity of free spacer^2)
2
Q
What is the equation for the electric field strength?
A
E = F/Q
3
Q
Define electric field strength
A
E at a point is the force on a positive unit charge placed at that point
4
Q
How do you find the resultant force on a point charge?
A
Sum of the force vectors
5
Q
Whats the unit of field strength?
A
V/m or N/C
6
Q
What do the field lines of a uniform field look like?
A
Parallel and equally spaced
7
Q
What is a source of field lines?
A
Positive charges
8
Q
What is a sink of field lines?
A
Negative charges
9
Q
How do field lines represent the strength of a field?
A
The closer the field lines the stronger the field
10
Q
What is an electric dipole?
A
A pair of equal and opposite charges separated by a fixed distance
11
Q
What happens to the static electric field inside a conductor?
A
The electrons move in such a way to cancel it out
12
Q
What is the vector p in relation to dipoles?
A
The electric dipole moment
p=Qd
13
Q
Which direction does the dipole moment point in?
A
From the negative charge to the positive charge
14
Q
When can there be an electric field inside a conductor?
A
If it carries an electric current
15
Q
Where does charge go on a conductor?
A
It sits on the surface
16
Q
Which way does the E field point from a conductor surface?
A
Perpendicular to the surface
17
Q
What is the equation of the E field perpendicular to a conductor surface?
A
E = (charge density)/(relative permitivity of free space)
= D/(permitivity of free space)
18
Q
Where on a surface is charge concentrated?
A
On the the areas with smallest curvature radius i.e. Corners and points
19
Q
Can conductors or insulators hold an electrostatic charge?
A
Only insulators can hold an electrostatic charge because electrons are held in place around the nuclei but can be polarised
20
Q
What equation governs the polarisation of a dielectric?
A
P=np where n is the number of atoms per unit volume and p is the dipole moment (P is also a vector)
21
Q
What is the equation relating electric flux density and electric field strength?
A
D=(relative permittivity of dielectric, epsilon r)(permittivity of free space, epsilon 0)E
22
Q
What are the boundary conditions of D (electric flux density) and E (electric field strength) at an interface between two materials?
A
- The parallel component of E is always the same on either side of the boundary
- The perpendicular component of D is the same on either side of the boundary if the boundary carries no free charge
23
Q
What is the area vector?
A
The area vector, S, has the magnitude of the surface area and points perpendicular to the surface
24
Q
What is the equation for electric flux in terms of the area vector?
A
electric flux = D.S
25
What is the equation for electric flux density in terms of the surface area?
DS cos(angle of field lines)
26
What are the units for electric flux density?
Coulombs
27
What does Gauss' law say about the total outward flux through a closed surface?
The total outward flux through a closed surface is equal to the total free charge enclosed in the surface
28
Write Gauss' law mathematically
electric flux = circular integral of D dS = Q
29
What is a Gaussian surface?
A closed surface around charges
30
Boobies?
Knockers
31
What are the rules when sketching lines of E
1) postive charges are sources, negative are sinks
2) arrow on line tells the direction of E
3) density of E lines is proportional to the magnitude of E lines
32
For a Gaussian surface containing no free charge what is the relationship between the lines of D leaving and entering the surface?
The lines of D leaving and entering the surface are equal.
| Lines of D cannot be created or destroyed within a GS containing no free charge
33
What is the difference between the E field of a free point in free space and in a dielectric?
In a dielectric the relative permittivity (epsilon r) has to be taken into account
34
Why is the E field smaller in a dielectric than in free space?
The relative permittivity (epsilon r) reduces the value due to the polarisation of the dielectric
35
What is D through the end plates of a cylindrical GS enclosing an infinite line of free charge?
Zero as D points radially out from the line of charge
36
What is the formula for D of an infinite line of charge through a GS?
D = (charge per unit length, lambda)/2*pi*r
| r is the radius of the GS
37
If a GS is half inside a charged metal and half in a dielectric what is the magnitude of the flux density perpendicular to the metal surface?
D = charge per unit area (sigma)
38
What is the boundary condition for D at an interface carrying charge?
D2 - D1 = charge per unit area (sigma)
D2 = D out of the GS
D1 = D into the GS
39
What is the boundary condition for E at an interface carrying charge?
The parallel component of E is always the same on either side of the boundary
40
What is the work done by the electrostatic field E in moving a change q between 2 points in a field?
W = - q (integral) E. dl
41
What does negative work mean?
the positive charge wants to move in the direction of the field
42
What is the potential difference by moving a charge of +1 C between two points?
V = W/Q
| = Q/4 pi E0 r
43
What is the electric potential?
Work done in moving +1 C from infinity to a specified point
44
What is the work done by moving a charge of +1 C between two points?
W = qV(ba)
| = q (delta B - delta A)
45
What is the charge induced on the outside of a grounded sphere with a positive external charge?
Negative charge
46
What is the charge induced on the outside of an isolated sphere with a positive external charge?
The surface nearest the external charge will become negative and the other side will become positive so that the total surface charge is zero
(Charge in an isolated system is conserved)
47
What is the differential form of Gauss' Law
dD(x)/dx = free charge per unit volume (phi(x))
48
What charges affect D?
Only free charges
49
Define potential difference
The work done in moving a charge of +1C between two points
50
Define electric potential at a point
The work done in moving a +1C charge from infinity to that point
51
What is the equation for electric potential?
phi = Q/4pi*(epsilon 0)*r
52
What are the units of electric potential?
Volts
53
What is the relationship between electric potential and electric field?
The magnitude of E is the negative gradient of the potential
| The direction of E is the direction in which the potential is decreasing
54
What is the equation for the relationship between electric potential and electric field in vector form?
E = -grad(phi)
55
Define an equipotential surface
A surface at which potential is constant at every point
56
Why must E fields be perpendicular to a conductors surface?
If two points on a conductor have different potentials there must be an E field
The field causes a force on the electrons in the conductor
The electrons will move to cancel out any potential difference
This means all points will have the same potential
The conductors surface is an equipotential
57
What direction does the E field go at any point on a equipotential's surface?
Perpendicular to the surface
58
What is the potential of an earthed conductor?
Zero
59
WHat is the charge on the surface of an uncharged isolated conductor?
Zero
60
WHat can be said about the potential on a charged isolated conductor?
It is constant and finite
61
What is the equation for the built-in voltage of a pn diode?
Vbi = 1/2(wn +wp)*Emax
| = [{q*W^2}/{2(epsilon0)(epsilon r)}]*[{Na*Nd}/{Na + Nd}]
62
What is the equation for capacitance?
C = Q/V
63
Define capacitance
Capacitance gives a measure of how efficiently a conductor system can store electrical charge
64
What are the steps for finding capacitance?
Find the field D between the conductors
Find E
Find V using E
Use V to find C
65
What is the equation for the capacitance of a capacitor made up of two spherical metal shells?
```
C = [4*pi*(epsilon0)*(epsilon r)*a*b]/[b-a]
a = radius of inner sphere
b = radius of outer sphere
```
66
Why can end effects be ignored?
WHen d<
67
What are end effects?
The presence of an electric field outside of a capacitor
68
What is the equation for capacitance in a parallel plate capacitor?
C = [A*(epsilon0)*(elsilon r)]/d
69
For a capacitor filled with two dielectrics (one on top of the other) what are D and E between the two dielectrics?
D is the same in both dielectrics
E is different in each dielectric
(permitivity of dielectric 1)*E1 = (permitivity of dielectric 2)*E2
70
Define a transmission line
Multiple long capacitors with a constant cross section along which electromagnetic signals can be propagated
71
Waht is the equation for capacitance for a coaxial cable?
C = [2*pi*(epsilon 0)*(epsilon r)*l]/[ln(b/a)]
72
What is the electrostatic energy stored in a capacitor?
U = 1/2 DEAd
73
What is the equation for electrostatic energy density of a capacitor?
Ue = 1/2 DE
74
NAme three types of capacitors
Impregnated paper
Ceramic
Variable air spaced
75
What is a varactor diode?
A pn junction diode which operates in reverse-bias
76
What are varactors used for?
Electronic tuning as part of communication systems
77
What is the equation for the capacitance of a varactor?
Cd = [{q*(epsilon r)*(epsilon 0)*A^2}/{2*(Vbi+Vr)}.{Na*Nd}/{Na+Nd}]^1/2
78
What is the equation for the small signal dynamic capacitance?
Css = 1/2 Cd
79
What is the breakdown field/dielectric strength?
The critical value of E at which sparking occurs leading to charge leakage and chemical breadown
80
Give an example of dielectric breakdown
Lightning is breakdown in the atmosphere
81
What does newtons 3rd law state?
forces on a wire are equal and opposite
82
Define magnetic flux density
Amount of magnetic flux in an area
83
What is the equation for magnetic flux density
dF2 = I2 (dL2 x B1)
84
What is the total force on the second wire?
F2 = I2 (L2 x B1)
85
What is the torque experienced in the coil of a motor?
T = N B I A sin (theta)
| Torque forces the coil to rotate about its axis
86
What is the force on each of the the vertical sections of a wire?
F = N B i L
87
What happens when theta > 0 and theta < 0
> 0 rotates clockwise
| < 0 rotates anti clockwise which stops it spinning
88
What does a Commutator do?
- Stops theta < 0.
| - reverses current when theta = 180 or 0.
89
How do you find electric flux density using BS law?
B = mu(0) I/ 2 pi R
90
What is the contribution to the flux density in the middle of a coil?
dB = (mu(0) I / 4 pi ) (dl/a^2)
91
What is the contribution to the flux density in the centre of a coil?
B mid = mu (0) I / 2 a
92
What is a magnetic dipole?
A circular loop of current
93
What is ampres law?
(circular integral) B . dl = mu (0) I
94
What does ampres law state?
The lien integral of B around the closed loop is equal to mu (0) times the total current threading the plane of the loop
95
What is B outside a long straight line using A law?
B(r) = mu (0) I/ 2 pi r
96
What is I inside long cylindrical wire using A law?
I (loop) = I r^2/a^2
97
What is B inside long cylindrical wire using A law?
B (r) = mu (0) I/ 2 pi a^2
98
What is B inside and outside of the wire?
- Inside it is proportional to r
| - Outside it is inversely proportional to r
99
What is a solenoid?
A long circular coil with many turns wrapped around a cylindrical former
100
What is B inside long solenoid using A law?
B(in) = mu(0) N I / L
| B is uniform inside and 0 outside
101
What happens to current between a pair of parallel sheets at low frequencies?
current is uniformly distributed across the width of the plates
102
What is B inside a pair of parallel sheets using A law?
B(in) = mu(0) I / W
103
What doesn't B depend on for a pair of parallel sheets?
-the surrounding plates, only the width of them
104
What is B inside a current carrying coaxial cable using A law?
B(r) = mu(0) I / 2 pi r
105
What is B outside of a coaxial cable?
0 as currents flowing on inner and outer conductors are equal and opposite so their is a finite flux density within the centre conductor
106
What is the magnetic flux measured in?
Wb or Tm^2
107
What is the equation for magnetic flux?
phi = BS
108
What is the equation for magnetic flux if B and S are vectors?
phi = BS (underlined) = BS cos (theta)
109
What is the magnetic flux when B is nonuniform?
phi = integral B. ds
110
What is self inductance?
current will produce a magnetic flux density B
| L = PHI / i
111
What is the flux linkage?
PHI = n phi
112
What is magnetic flux for a long solenoid?
phi = BA = mu(0) N I A / l
113
What is L for a long solenoid?
L = mu (0) N^2 A / l
114
What is the turns per unit length?
n = N / l
115
What is the flux linkage for parallel plates?
PHI = mu(0) l dF/ W
116
What is L for parallel plates?
L = mu(0) dl / W
117
What is the flux linkage for a coaxial cable?
PHI = mu(0) i L/ 2 pi *ln (b/a)
118
What is L for a coaxial cable?
L = mu(0)l / 2pi * ln (b/a)
119
At low frequencies what happened to the current on a coaxial cable?
current on the centre conductor is uniformly distributed across the surface
120
At high frequencies what happened to the current on a coaxial cable?
current is forced to flow in a very thin layer
121
What is mutual inductance?
When the current in the first circuit produced a flux linkage that cuts the plane of the second circuit
122
What does M21 equal?
M21 = PHI2 / I1 = M12
123
What is faradays law?
v = - dphi/ dt
124
What is the voltage developed across an inductor?
v = - L di / dt
125
What is the voltage developed in the later circuit?
V 2 = -dphi2/dt = -M di1/dt
126
What does the current in an indictor do?
- lags by 90
| - builds up from 0 until it reached a stead (DC) value I
127
What is the rate of working P of DC power against voltage induced across the inductor?
P = i. L di/dt
128
What is the total work done by the power supply again induced voltage?
W = 1/2 L I^2
129
What is the work done by the power supply in converting into stored energy in the inductor?
U = 1/2 L I ^2
130
What is the magnetic engird density equation?
U(m) = B(in) ^2/ 2 mu(0) *(V solenoid if for a solenoid)
131
What is the field energy density associated with?
The energy required to set up B in the first instance
