Magnetism, EM induction and AC

Question 1

Right hand grip rule

Answer 1

Fingers: field
Thumb: current

Question 2

Force formulas

Answer 2

Force on charge carrying wire
F = B I L sinθ
Force on charged particle
F = B Q v sinθ

Question 3

Magnetic flux density meaning

Answer 3

Force experienced by a straight current carrying conductor at right angles to that field per unit length and unit current

Question 4

1 Tesla is…

Answer 4

when a current carrying wire of 1m length with 1A current placed at at a right angle to a magnetic field experiences a force on 1N

Question 5

Left hand rule

Answer 5

Thumb: force
Index: field
Middle: current

Force goes in opposite direction if electrons are considered instead of current

Question 6

Centripetal force provided by magnetic force

Answer 6

Fc = Fn
mv²/r = B Q v sinθ
r = m v sinθ / Bq

Question 7

Hall effect formulas

Answer 7

Vʜ = I B / n q t

I is current
B is magnetic flux density
n is number charge density
q is elementary charge
t is thickness of the waver

Question 8

Conservation of energy with Hall effect;
lots of formulas

Answer 8

Fe = q E

q is elementary charge
E is electric field strength

W = Fe x d = Vʜ x q

v = E / B
v (velocity of charged particle)
E (electric field strength)
B (magnetic field strength)

E = V / d
E (electric field strength)
V (pd between 2 points)
d (distance between 2 points)

Question 9

Lenz’s law definition

Answer 9

any induced current or induced emf will be established in a direction so as to produce effect which oppose the change that is producing it

Question 10

Right hand rule generator edition

Answer 10

Thumb: force applied to cause motion
Index: magnetic field
Middle: current inside conductor

Used when force makes current

Question 11

Lenz’s law conservation of energy and key formula

Answer 11

W = F x
W = P ∆t
ε = B L v N

ε is emf across conductor

Question 12

Magnetic flux linkage

Answer 12

ψ = B A cosθ N

ψ flux linkage
B magnetic field density
A area linked to magnetic field
N number of loops

Question 13

Faraday’s law definition

Answer 13

magnitude of induced emf is proportional to rate of change of magnetic flux linkage

Question 14

Faraday’s law emf formulas

Answer 14

ε = - [ ∆ψ / ∆t ] N

Question 15

Generating AC currents

Answer 15

flux
ψ = BA cos(ωt)

emf
εₜ = ε₀ sin(ωt)

pd (with closed circuit)
Vₜ = V₀ sin(ωt)

current
Iₜ = I₀ sin(ωt)

(V = RI and θ = ωt)

Use cos if variable starts at max when crossing origin and use sin if variable starts at zero when crossing origin

Question 16

AC- Power formulas

Answer 16

peak power:
P₀ = V₀² / R
or
P₀ = I₀² x R

mean power:
Pₐᵥ = 0.5 x V₀² / R = V²ᵣₘₛ / R
or
Pₐᵥ= Iᵣₘₛ² x R = 0.5 x I₀² x R

root mean square:
Vᵣₘₛ = V₀/√2
Iᵣₘₛ = I₀/√2

Question 17

Transformers

Answer 17

Vs/Vp

Ns/Np
=
Ip/Is

Question 18

Flux

Answer 18

Amount of magnetism, unit: Wb

Question 19

Flux density

Answer 19

How tightly packed together are the field lines
B, unit: T (tesla)

Question 20

Direction of current into or out of plane

Answer 20

Dart method
Dot: into plane
Cross: out of plane

Question 21

Additional flux formula

Answer 21

B = mg/IL

Question 22

Emf and flux graphs against t - for coil entering and exiting uniform magnetic field

Answer 22

phi / t
zero grad at zero
constant positive grad
zero grad at constant
constant negative grad
zero grad at zero

• emf / t
  zero grad at zero
  vertical upwards
  zero grad at constant
  vertical back to zero
  zero grad at zero
  vertical downwards
  zero grad an negative constant
  vertical back to zero
  zero grad at zero

Question 23

Stationary coils

Answer 23

In order to induce emf, flux density over time must be changing as area of coil remains constant

Question 24

Flux linkage

Answer 24

Same as flux but with multiple turns hence formula is
Flux linkage = BAN

Question 25

Eddy currents and transformers

Answer 25

By laminating or cutting transformer into layers this reduced eddy currents and heating effect to increase efficiency of transformer

Question 26

Eddy currents

Answer 26

Eddy currents are electric currents that circulate within a conductor and are induced when a conducting material is exposed to a changing magnetic field. Eddy currents can create resistance and heat within the conducting material.

Question 27

AC generation and flux

Answer 27

flux is zero and emf is at a maximum when coil is parallel to field

flux is at a maximum and emf is zero when coil is perpendicular to the field

Question 28

Flux time and emf time graph for AC generation

Answer 28

phi / t
sinusoidal graph where peak at max and min are equal to BAN and -BAN respectively

emf / t
sinusoidal graph where peak is at zero for phi and zero is at peak for phi, max is ε₀

emf and flux (linkage) are 90º out of phase

Question 29

AC and diodes

Answer 29

Voltage with dc current gives full sinusoidal graph

Half wave rectification: With a diode it gives sinusoidal graph discarding any negative directions

Full wave rectification: 4 diodes in a diamond arrangement which gives the half wave rectification graph excluding the gaps

Smoothed rectification with capacitor: initial sinusoidal curve into ripple (produced with capacitor and resistor)

Question 30

Magnet in free fall through solenoid graph

Answer 30

ε against t

increasing grad
decreasing positive grad
zero grad
decreasing negative grad
zero
sharp negative grad and smooth curve into sharp positive grad back to zero

Vf > Vi
|+ε max| < |- ε max|

Question 31

Time for proton to complete a full circle

Answer 31

If field is large enough:
T = 2πr / v
r = mv/Bq

Question 32

Additional formulas from Kwon’s notes

Answer 32

q/m = v / rB
e/m = 2V / r²B²
ε = ω N B A sinθ

Recall:
ω = 2πf