Electromagnetic Induction (topic 5, 10, 11)

Question 1

Coulomb’s law

Answer 1

Force between two charges at a distance ‘r’ apart

Question 2

Coulomb’s law equation

Answer 2

F = k q1q2 / r^2

where
F = force (N)
k = constant
q1 = charge 1 (C)
q2 = charge 2 (C)
r = distance between charges (m)

k = 1 / 4πε0

Question 3

Electric field strength

Answer 3

E = F / q

where
E = electric field strength (NC^-1)
F = force (N)
q = charge (C)

Question 4

Current

Answer 4

Number of coulombs going by per second

Question 5

Moving charge

Answer 5

I = Δq / Δt

where
I = current (A)mperes)
q = charge (C)
t = time (sec)

Question 6

Drift velocity equation

Answer 6

I = nAvq

where
I = current (A)
n = # of electrons per unit volume (m^-3)
A = cross sectional area (m^2)
v = drift velocity of electrons (ms^-1)
q = charge (C)

Question 7

Potential difference

Answer 7

To move a charge around, you need to do work. The potential difference is the work done per charge

**use p.d. instead of voltage

Question 8

Potential difference equation

Answer 8

V = W / q

where
V = potential difference (V)
W = work done (J)
q = charge (C)

Question 9

Resistance equation

Answer 9

R = V / I

where
R = resistance (Ω)
V = potential difference (V)
I = current (A)

Question 10

Resistivity

Answer 10

ρ = RA / L

where
ρ = resistivity
R = resistance (Ω)
A = cross sectional area (m^2)
L = length of wire (m)

Question 11

Power

Answer 11

Power dissipated = energy lost in heating up

P = V I = I^2 R = V^2 / R

where
P = power (W or Jsec^-1)
V = potential difference (V)
I = current (A)
R = resistance (Ω)

Trick:
Power = work / time = energy / time

Question 12

Internal resistance

Answer 12

Batteries have their own internal resistance that eats away at some of the volts
**emf is not a force. It is a p.d. measured in volts

Question 13

Internal resistance equation

Answer 13

ε = I (R + r) or ε = IR + Ir

where
ε = electromotive force (V)
I = current (A)
R = resistance (Ω)
r = internal resistance of the battery (Ω)

IR = what you get (V)
ε = what the battery tries to give you (V)
Ir = lost by internal resistance of the battery (V)

Question 14

Magnetic field

Answer 14

Where the north on a compass would point

Question 15

Moving charge in a magnetic field

Answer 15

F = qvB sinθ

where
F = force (N)
q = charge (C)
v = speed (ms^-1)
B = magnetic field strength (T)esla)
θ = angle between B and v (°)

**if sin 90° (perpendicular), then = 1

Question 16

Wire in a magnetic field

Answer 16

F = BIL sinθ

where
F = force (N)
B = magnetic field strength (T)esla)
I = current in a wire (A)
L = length of the wire (m)
θ = angle between B and I (°)

**if sin 90° (perpendicular), then = 1

Question 17

Wire with a current (hand rules for magnetic fields)

Answer 17

Use RHS rule (thumbs up)
thumb = current = I (A)
fingers = magnetic field B (T)

Question 18

Solenoid (coil of wire) (hand rules for magnetic fields)

Answer 18

Use RHS rule (thumbs up)
fingers = current = I (A)
thumb = magnetic field B (T)

Question 19

Moving charge (or wire (current)) in a magnetic field (hand rules for magnetic fields)

Answer 19

Use LHS rule for negative charges (flat palm)
fingers = magnetic field B (T)
palm = force
thumb = velocity of particles (or the current)

Use RHS rule for positive charges or current (flat palm)
fingers = magnetic field B (T)
palm = force
thumb = velocity of particles (or the current)

Question 20

Gravitational and electrical potential equations

Answer 20

Respectively:
Vg (J kg^-1) = -GM / r

Ve (V or J C^-1) = kQ / r

Question 21

Gravitational and electrical field strength equations

Answer 21

Respetively:
g (N kg^-1) = -ΔVg / Δr

E (N C^-1) = -ΔVe / Δr

Question 22

Gravitational and electrical potential energy equations

Answer 22

Respectively:
Ep (J) = mVg = -GMm / r

Ep (J) = qVe = kQq / r

Question 23

Gravitational and electrical force equations

Answer 23

Respectively:
Fg (N) = GMm / r^2

Fe (N) = kQq / r^2

Question 24

Gravitational and electrical work equations

Answer 24

Respectively:
W (J) = mΔVg

W (J) = qΔVe

Question 25

Equipotential lines

Answer 25

Where Vg and Ve are the same

Question 26

Orbital mechanics

Answer 26

In an orbit, a satellite of mass m around a planet (mass M) has an orbital radius r

Question 27

Escape velocity

Answer 27

To completely leave a system’s gravitational field, you need to go to a distance of infinity. So at infinity, total energy = 0

**escape velocity is the minimum speed you need to reach r = infinity

Question 28

Orbital speed

Answer 28

A satellite of mass m orbits a central mass M

Question 29

Magnetic flux

Answer 29

Φ = BA cosθ

where
Φ = magnetic flux
B = magnetic field strength (T)
A = area (m^2)
θ = angle between B and the normal to A

Question 30

Faraday’s law

Answer 30

ε = −N ∆Φ / ∆t

where
ε = induced emf (V)
N = # of turns in the coil
∆Φ / ∆t = rate of change of magnetic flux linkage

Question 31

Moving wire in a magnetic field equation

Answer 31

ε = Bvl

where
ε = induced emf (V)
B = magnetic field strength (T)
v = speed of the wire (ms^-1)
l = length of the wire (m)

Question 32

Alternating current (ac)

Answer 32

Current generated (induced) alternates in direction because of Lenz’s / Faraday’s laws

Question 33

Maximum power (ac)

Answer 33

Pmax = I0 V0

where
Pmax = maximum power (W)
I0 = maximum current (A)
V0 = maximum p.d. (V)

Question 34

Average power (ac)

Answer 34

P (line on top) = 1/2 I0 V0

where
P (line on top) = average power (W)
I0 = maximum current (A)
V0 = maximum p.d. (V)

Question 35

Current graph AC

Answer 35

I(rms) = I0 / √ 2

where
I(rms) = root mean square current
I0 = maximum current (A)

**avg. current = 0
**sin graph (I vs t)

Question 36

Potential difference (“voltage”) AC

Answer 36

V(rms) = V0 / √ 2

where
V(rms) = root mean square p.d.
V0 = maximum p.d. (V)

**avg. p.d = 0
**sin graph (V vs t)

Question 37

Ohm’s law for AC

Answer 37

R = V0 / I0 = V(rms) / I(rms)

where
R = resistance (Ω)
V0 = max. p.d. (V)
I0 = max. current (A)
V(rms) = root mean square p.d. (V)
I(rms) = root mean square current (A)

Question 38

Transformers and rectification

Answer 38

εp / εs = Np / Ns = Ip / Is

where
εp = primary p.d. (V)
εs = secondary p.d (V)
Np = number of turns in primary
Ns = number of turns in secondary
Ip = current in primary (A)
Is = current in secondary (A)

**go from small N to large N (step up)
**gives larger p.d. in secondary

Question 39

Half-wave rectification (one diode)

Answer 39

In a wave graph, the negative values become zero. (^_ ^_ ^_) (rectified but not smooth)

Adding a capacitor:
(^- ^- ^-) (rectified and smooth)
**happens once per period / cycle

Question 40

Diode

Answer 40

Only lets current in one direction through

Question 41

Capacitor

Answer 41

Smoothes the curve because it can charge up while current flows through diode, but when current stops in diode, capacitor discharges into resistor. Smooths out the waves.

It can charge and discharge in a circuit (like a mini battery)

Question 42

Rectification

Answer 42

The conversion of an alternating current to a direct current

Question 43

Full wave rectification (two diodes)

Answer 43

You need two diodes and a ‘center tap’ on the secondary (^^ ^^ ^^)

**happens twice per period / cycle
**need twice the number of coils to do thid instead of half-wave rectification

Question 44

Full wave rectification using a diode bridge

Answer 44

Advantage: need less coils in secondary
Disadvantage: more diodes and more gross looking circuit

shows the same as a normal full wave rectification (^^ ^^ ^^)

Question 45

Capacitor equation

Answer 45

C = q / V

where
C = capacitance (F)
q = charge (C)
V = p.d. (V)

Question 46

Parallel plate capacitor equation

Answer 46

C = ε A / d

where
C = capacitance (F)
ε = permittivity
A = area of each plate (m^2)
d = separation between plates (m)

Question 47

Dielectric

Answer 47

Reduces V, increases C

Question 48

Discharging capacitors

Answer 48

If the capacitor is charged, when you close the switch it will discharge

Question 49

The charge in the capacitor equation

Answer 49

q = q0 e^(-t / τ)

where
q = charge remaining (C)
q0 = initial charge (C)
t = time elapsed (sec)
τ = time constant (t)

Question 50

Time constant equation

Answer 50

τ = RC

where
τ = time constant (t)
R = resistance (Ω)
C = capacitance (F)

Question 51

Energy stored in a capacitor

Answer 51

E = 1/2 CV^2

where
E = energy stored (J)
C = capacitance (F)
V = p.d. (V)