Electromagnetism Year 2

What is the equation for Coulomb’s Law?

r^ is a unit vector along r

How do you extend Coulomb’s Law for 3+ charges?

use superposition

How do you deal with continuous charge distributions with Coulomb’s Law?

Integrate

What are the 2 steps to split up and solve electrostatic problems?

1) Find electric field due to collection of charges

2) Charges then interact with this electric field

What is the equation used in the first step of solving an electrostatic problem?

What is the equation in the second step of solving an electrostatic problem?

What is the equation for the electric field due to a point charge Q?

What is Gauss’ Law?

For any charge distribution

circle means closed surface, S refers to surface

What is the wordy version of Gauss’ Law?

"The outward flux of E over any closed surface is equal to the algebraic sum of the charges enclosed by the surface divided by ε_0”

At equilibrium what is the electric field inside a conductor?

0

What is the equation for ∆U (change in potential energy) for when 2 charges Q₁ and Q₂ are initially separated by r₁ then an external force changes their separation to r₂?

What is the equation for potential energy for 2 charges?

What is the change in potential energy for tangential displacement of charges?

∆U=0 for tangential displacement

If potential energy of a system varies by U_BA as a test charge Q_t is moved from point A to point B, what is the potential difference V_BA between points A and B defined by?

What are the SI units for electric potential?

J/C

What is the equation for the change in potential energy of a charge Q when moved through a potential difference V?

What is the equation for the electric potential produced by a point charge at a distance r from the charge?

What is the equation for the total potential at a point for a system of N charges?

What is the full vector equation of electric field?

What is the physical significance of the gradient of the electric field?

At any point the gradient of a function of points in the direction corresponding to that for which the function varies most rapidly 

The magnitude of the gradient vector gives the size of this maximum variation

What is the defining equation for Capacitance?

What is the equation for potential energy stored by the capacitor?

What is the equation for energy density, u?

What is the differential form of Gauss’ Law? (for in a vacuum)

What does the following refer to?

“At any point in space the divergence of the E-field is equal to the  charge density at that point divided by epsilon nought”

Gauss’ law for electric fields in differential form

The first of Maxwell’s equations

What can divergence be thought of as?

giving the number of field lines starting(if divergence is positive) or terminating(if divergence is negative) at a given point

What is the physical significance of the divergence for electric fields?

Can think of the divergence as a vector as telling us how much of the vector field starts or terminates at a given point

What is the equation for the electric potential difference between two points?

What is the equation for electrostatic fields for the line integral of E around any closed path?

What is the curl of E equal to?

What is Poisson’s equation for electrostatic fields?

What is Laplace’s equation for electrostatic fields?

(when rho=0 in Poisson’s equation)

What is an electric dipole an example of?

A system that is overall electrically neutral but still produces an electric field and is affected when placed in an electric field

Happens due to the positive and negative charges being physically separated

What are 2 equations for the potential of an ideal electric dipole?

What is the equation for the electric field of an ideal electric dipole?

What is the equation for the electric dipole moment in vector form?

p = Qs

What is the torque direction of an electric dipole given by?

The right hand screw rule

What is the equation for torque on an electric dipole in an electric field?

T=pxE 

How do you choose energy configuration for a dipole in an electric field?

Choose when both charges are on the same equipotential line so total energy is zero

What is the equation for work done on a dipole in an electric field?

Work done = Torque x angle

What is the potential energy of a dipole in an electric field at an angle θ?

What is the equation for the force on a dipole in a non-uniform electric field?

How much does capacitance increase by when the region between plates is filled with a dielectric?

increases by a factor ε_r

What is ε_r? 

Relative permittivity of the dielectric

Is ε_r constant?

Sometimes but for some materials it is not constant and can vary with temperature and frequency

How does the dielectric increase the capacitance?

By reducing the size of the E-field

What is the definition of polarisation, P?

The amount of electric dipole moment per unit volume

What is the equation for the total electric dipole moment?

Pdτ

What are the units of polarisation?

C m^-2

What is the magnitude of polarisation proportional to?

applied electric field

Draw a diagram showing the polarisation field, applied electric field, the surface charge density, and the direction of the dipoles in a dielectric

What is surface charge density, σ_p, always numerically equal to?

The normal component of P

What is the equation for the D field?

D=ε₀E+P

What are the units of the D field?

Cm^-2

What is Gauss’ Law in terms of D?

What affects the D field?

Free charges only

What is the equation for the D field strength?

What is the equation relating P and E?

What is the equation relating relative permittivity and electric susceptibility?

How do you modify electrostatic equations in the presence of dielectrics?

Replace ε₀ with ε₀ε_r

What is the breakdown field for a dielectric?

The maximum E-field that can be applied before the dielectric starts to conduct an electrical current

Above this field the dielectric no longer acts as an insulator

What does dielectric breakdown limit?

Limits the energy that can be stored in the a capacitor

What are the boundary conditions for D and E at the interface between 2 dielectrics?

There are E and D fields on either side of the interface

If there is no free charge at the interface then:

• The normal component of D is continuous

• The tangential component of E is continuous

What are the two steps for solving a magnetism problem?

Find field due to current elements

Find magnetic force due to the field

What is the Biot-Savart law?

What is Ampere’s circuital law?

What is the general result obtained from the differential form of Ampere’s circuital law?

What is the equation for the magnetic force acting on a current element or moving particle?

dF = IdLxB 

What are the two equation for the magnetic force for a charged particle moving with a velocity v in a field B?

What are the two equations for torque for magnetic dipoles?

where A is the vector corresponding to the area of the circuit and B is the magnetic field

What is the consequence of the non-existence of magnetic monopoles?

No magnetic equivalent of single charges, so no sources or sinks of the B-field

Means that B field lines are continuous and have no start or end

What is the integral form of Gauss’ Law for B-fields?

What is the differential form of Gauss’ Law for B-fields?

Why is Gauss’s Law less helpful for B-fields than for E-fields?

Because they have zeros in them

When is an electromotance induced as determined by Faraday’s experiments?

A rigid stationary circuit is placed in a time varying magnetic field

A rigid circuit moves in a steady B-field such that the magnetic flux through the circuit changes

Part of a circuit moves and in doing so cute magnetic flux

What does Lenz’s law do?

Gives direction to the induced electromotance or current

What does Lenz’s law state?

Whenever a change produces an induced current, the direction of flow of this current is such as to oppose the change causing it

What is the the flux for a magnetic field through A when B is constant?

Φ = B.A

What is the the flux for a magnetic field through A when B is not constant?

What is the wordy definition of electromotance?

The energy or work done per unit charge when it is moved around a closed path L

What is the definition equation of electromotance?

What are the other names for electromotance?

Voltage

Potential difference

Electromotive force

What are the units of electromotance?

Volts, V

What is the equation that means that static charges are unable to produce an electromotance?

What is Faraday’s law of electromagnetic induction?

The negative sign is added to satisfy Lenz’s law

What is the equation for the total E field?

E_tot = E_s+E_M

What is the Fourth Maxwell equation?

The differential form of Faraday’s law

What is the divergence of E_M?

What is the equation for div E_tot for electromagnetic fields?

same as for purely electrostatic fields since div E_M = 0

What does self-inductance describe?

Describes how flux caused by the magnetic field (induced by a current in a circuit) affects the circuit, particularly when it changes

What is self inductance?

The constant of proportionality between magnetic flux and current

What is the equation for self-inductance?

What are the units of self-inductance?

Henry (H)

What is an inductor?

A device designed to exhibit a specific value of self-inductance

What is the electromotance produced given by when the current through a circuit changes?

What does the negative sign in this equation indicate?

That the direction of the induced voltage opposes the change in current

For a solenoid helically wound with a length much greater than its diameter, what is the value of the field?

Pretty much constant

µ₀nI

where n is the number of turns per unit length

What is the flux across each turn of area A of a solenoid helically wound with a length much greater than its diameter?

Aµ₀nI

What is the total flux for a solenoid length l?

What is the equation for self-inductance for solenoids?