Electrostatics equations

Question 1

What links force, charges in the field and radius?

Answer 1

F = k QQ/r^2 - Coulomb’s law

Question 2

What 4 key properties does the electric force between charges have?

Answer 2

Like charges repel. Force acts along line between charges. Magnitude of force is inversely prop. to square of distance between charges. Force is proportional to product of charges magnitude

Question 3

What links amps, coulombs and seconds?

Answer 3

1 Amp = 1 C/s

Question 4

What shape is force distributed from a point charge?

Answer 4

Radially/Sphere

Question 5

Why do we add epsilon r into Coulombs law?

Answer 5

Because the material affects force so the relative permittivity of the surrounding material is included.

Question 6

What is Coulomb’s Law for two isolated point charges?

Answer 6

F = Q Q / 4πr^2 ε0εr

-Force here is a vector

Question 7

What is ε0?

Answer 7

Permitivitty of free space(vacuum) (8.854x10^-12 C^2/NM^2)

Question 8

What is εr?

Answer 8

Relative permittivity of the surrounding material (dimensionless) (=1 for free space)

Question 9

What is the principle of superposition for charges?

Answer 9

Where multiple charges are present, the force experience by any charge is the vector sum of the forces on it from other charges.

Question 10

What links Electric field, force and a test charge?

Answer 10

E = F/Qt

-E and F are vectors

Question 11

For isolated charges what links Electric field strength, charge and radius?

Answer 11

E(vector) = Q/4πr^2 ε0

Question 12

What do radial field lines show?

Answer 12

The direction of force for a positive test charge in that field.

Question 13

What is an electric dipole?

Answer 13

Electric dipoles are pairs of equal but opposite point charges separated by some small fixed distance.

Question 14

What equation for a dipole, links Torque, Electric field, charge and distance?

Answer 14

𝜏+ = 𝜏− = 𝐸𝑄(𝑑/2)sin 𝜃, therefore total torque on dipole is 𝜏 = 𝐸𝑄𝑑sin 𝜃

Question 15

What links work, force and displacement?

Answer 15

Work = Force x displacement

Question 16

What is an equation for Potential Energy with charges.

Answer 16

Work = Potential Energy = − ∫ 𝐸⃗ 𝑄𝑡 .𝑑𝑟⃗

Limits Ra and ∞

Question 17

What links potential, charge and distance?

Answer 17

Potential =𝑄1 / 4𝜋𝑟 𝜀0

-Divide potential energy by Qt.

Question 18

What is an equation for potential difference using two points a charge has moved between (rA and rB)?

Answer 18

Potential difference = − ∫ 𝐸⃗ .𝑑r

Limits rB and rA

Question 19

What links Electric flux density, D(vector) and electric field strength?

Answer 19

D(vector) = 𝜀0𝜀r E(vector)

Question 20

What links electric flux, electric flux density and area?

Answer 20

𝜓 = 𝐷⃗𝐴 cos θ

Question 21

What is Gauss’ Law in words?

Answer 21

“the total electric

flux out of a surface is equal to the net charge enclosed by that surface”

Question 22

What is Gauss’ Law, using S(closed surface), D(electric flux density), ψ(flux out of the surface), Q(charge enclosed)

Answer 22

ψ = ∯𝐷⃗𝑑𝑆⃗ = ∑𝑄𝑒𝑛𝑐

Question 23

What is Gauss’ Law reduced for a Gaussian surface?

Answer 23

ψ = 𝐷𝑛𝑆 = ∑𝑄enc

Question 24

Explain how to find electric field strength from Gauss’ Law for spherical Gaussian surface.

Answer 24

1. ψ = 4𝜋𝑎^2𝐷 = 𝑄
2. 𝐷 = 𝑄4𝜋𝑎^2
3. 𝐸⃗ =𝐷⃗/𝜀0𝜀𝑟 = 𝑄/4𝜋𝜀0𝑎^2

Question 25

What is capacitance?

Answer 25

A measure of a systems ability to store energy in an electric field.

Question 26

What links capacitance, charge and voltage?

Answer 26

C = Q/V units Farads

Question 27

What does capacitance depend on?

Answer 27

The physical properties of the system (its dimension and materials)

Question 28

What links energy stored by a capacitor, Q, C and V

Answer 28

Energy stored = 1/2 Q^2/C = 1/2 QV = 1/2 CV^2

Question 29

What links capacitance, area of plates, distance between them?

Answer 29

𝐶 = 𝐴𝜀0 / 𝑑

Question 30

What is a dielectric material?

Answer 30

An insulator. In an electric field molecules within the material align their dipoles to produced a polarised material.

Question 31

What links the electric field strength and electric flux density with dielectric materials?

Answer 31

E = D/𝜀0𝜀r

Question 32

What is the charge enclosed within a conducting sphere?

Answer 32

It is zero. Therefore flux density and electric field are also zero.

Question 33

What is the capacitance per metre for a Gaussian cylinder?

Answer 33

𝐶 = 2𝜋𝜀0𝜀𝑟 / ln(𝑏/𝑎)