QUIZ ONE REVISION Flashcards by Romane Bouchard

What is the force between two point charges separated by d?

Coulomb’s law for point charges

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What is a field?

How is electric field related to the electric force?

Scalar: assignment of a scalar to each point in region in space (eg. Temperature field)
Vector: assignment of a vector to each point in region in space (eg Moving fluid field: each point has a velocity)

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How to compute electric field @ a random point generated by many charges at different locations?

Principle of superposition.

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What is the electromagnetic force on a moving charge?

F = q(E + uxB)

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What is the basic element of the Electric field/Magnetic field?

Electric field: charges

- Magnetic field: current

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A magnetic compact is placed
-above a current carrying wire
-below a current carrying wire
what will happen?

Will rotate to align with the magnetic field direction which is opposite at above and below.

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What is carrying the current in metallic wires?

Electrons of valence of the metallic material.

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Maxwell’s equation:

Flux of E through closed surface
Flux of B through closed surface
Circulation of E around closed curve
Circulation of B around closed curve

-enclosed charge/epsilon ∇ • E = ρ/ε
-0 ∇ • B = 0
- (-)d/dt (flux of B through S bounded by the curve)
∇ × E = ∂_t B (Faraday’s)
∇ × E = 0 (electrostatics
- d/dt (flux of E through S bounded by the curve + flux of current through C/epsilon
∇ × B = μJ + (1/c^2)∂_t E

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What is the divergence of a vector field?

∇ • E : measures of a spread of E from a point

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What is the curl of a vector field?

∇ × E : measures how electric field swirls around a point (local rotation)
0 in electrostatics

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What is the divergence theorem?

Surface integral of flux ( E • n) = volume integral of divergence (∇ • E)

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What is Stoke’s theorem?

Circulation of Vector Field (Vector Field • dl) = surface integral or curl of vector Field (∇ × Vector field)
-for Electrostatics this = 0

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Explain and derive F = 1/r^2 r-hat

guess: ∇ • F = 0 but flux of F = 4π
∇ • F = 1/r^2 ∂_r r^2 (F) = 0 for r not 0
So, we define ∇ • F = 4πδ^3(r)

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Electric potential units?

Volts

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How do electric potential lines look like?

Equipotential lines perpendicular to electric field lines

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How is work done by moving a charge from point A to point B related to potential?

W = QΔV = -integral(AtoB) QE dl

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What is the electric field around an infinite plane of uniform charge density sigma?

E = sigma/2ε n-hat

-constant since the further you are from the plane, the more charges you see

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What does the graph of a sphere of uniform charge density look like?

proportional to r inside (grows because see more charges)

proportion to 1/r^2 outside (like point charge

Why do we say that the electric field inside a conductor is zero?

Because we are in electrostatics. If E is not 0 then the electrons would be free to move inside.

what is Poisson’s equation?

∇⋅(-∇𝑉)=ρ/ε so ∇^2V=-ρ/ε

Define dipoles. How are they related to dielectrics (insulators)

When d

Sketch of electric field due to dipoles

Field lines loop

What is the force on a dipole with uniform external field?

Fnet = 0 but net torque such that dipole moment align with external field

Why do balloons stick to animal fur?

Force of the dipole is proportional to the dipole moment and Electric field. Both get greater (so is the force) as get closer to the fur

When the total charge distribution is non-zero, what is the leading term of V scaled with r?

Vmonopole is proportional to 1/r

When total charge distribution is zero, how is the two leading terms scaled with r?

dipole: 1/r^2 quadruple: 1/r^3

Which property of differential equations allow us to use the method of images?

Uniqueness theorem

What should be the total charge on the surface of a conductor if it is grounded and there is a charge q in front of it?

-q

What is the force on the point q?

It is Coulomb's law between q and -q with a distance of 2d towards the conductor sheet

Is the potential necessarily zero inside a conductor?

No because the method of image gives the potential outside. But you know that E=0 inside. So V is constant inside

How is Poisson's equation (Laplace) written in terms of separation of variable?

V = X(x)Y(y) -> damped in one axis and oscillation in the other axis

What is the general solution to the laplace equation in spherical coordinates?

Return to multipole expansion (monopole,dipole,quadruple...)

What is the electrostatic potential of a conducting sphere in uniform electric field?

Far from the sphere: external field | Close to the sphere: dipole induced by external field with p = 4πεR^3E

Does electrostatic energy obey the principle of superposition?

No W = ε/2 integral (E^2 dV)

How do you calculate the Bond energy of a metal?

1/(4πε) (e^2/a) where a is the atomic spacing.

What is meant by magnetostatics?

1) Steady current | 2) Derivative with time of B = 0 such that curl of E = 0

What is the unit of a steady current

A/m^2

How do charge particles behave in magneticfields?

By right hand rule: circle around B | Magnetic force is F = q(u x B)

How do the leading term of magnetic field scale with distance?

B dip is proportional to 1/r^3

How would you compute the magnetic field around a current carrying wire?

Ampere's law: azimuthal symmetry | Curl of B = circulation of b around closed curve = µJ

How would you compute the magnetic field around a planar current sheet?

Rectangular loop that straddles the sheet | k = di/dl = sigma u

What is the magnetic field around a solenoid?

``` Outside = 0 inside = µnI ```

How is B related to vector potential?

B = ∇ × A since ∇ • B = 0 (always true). This is not a unique vector potential. (Defined to a gradient of some vector field)

What happens to a current carrying loop in a uniform external magnetic field?

There will be net rotation (torque) such that the magnetic moment of the loop and b align