Magnetic fields Flashcards by Henry Triff

What is Maxwell’s corkscrew rule / right hand rule?

This shows the direction of the magnetic field around a current carrying wire.
> Thumb - Direction of current
> Fingers - Direction of magnetic field

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What is the symbols used for the magnetic field moving in and out of the plane of the paper?

> Out of the paper: ⊙

> In to the paper: ⊗

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What is Flemmings left hand rule?

This shows the force applied to a current carrying wire placed into a magnetic field:
> Thumb - Force / Motion
> First finger - Magnetic field
> Second finger - Current

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What is the equation that comes from Flemmings left hand rule?

F = BILsinθ

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How can the equation F = BILsinθ be combined with current density and simplify it?

F = BAneVdLsinθ
N = nAL (Number of electrons)
q = Ne
F = BqVdsinθ

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What is the hall effect?

> When current flows through a wire in a perpendicular magnetic field
Electrons experience a force perpendicular to their motion
This causes electrons to accumulate onto one face of a material giving it a negative charge
This produces an electric field within the wire which balances the magnetic field
The hall voltage can be measured across the two faces of the wire

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How is the hall voltage used?

It is used to calculate the carrier density:
> E = - dV/dx - This can be measured
> F = BqVd => Eq = BqVd => E = BVd
> E = BVd - The magnetic field is known so Vd is calculated
> I/A = neVd => I/AeVd = n
- The Current and crossectional area can be measured
- The electron charge is known
- The Vd is calculated so the number density can be calculated

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What is Lenz’s law?

‘The induced current flows always in such a direction as to oppose the change causing it’

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What is the Magnetic flux density?

The magnetic flux per unit of area
> Symbol: B
> Units: Tesla

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What is magnetic flux?

The quantity of magnetic flux from a magnetic / electromagnet
> Symbol: ϕ

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What is the equation to calculate the magnetic flux?

ϕ = BAcosθ or ϕ = NBAcosθ
θ = the angle between the direction of the magnetic field and the perpendicular to the face of the area

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What is induced EMF?

This is the voltage induced into a wire when it is moved through a magnetic field.
> Symbol: V

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What is the equation to calculate induced EMF?

V = - dθ/dt

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Why is there a negative in the equation used to calculate induced EMF?

Because of Lens’z law

THIS IS IMPORTANT

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What affects the magnitude of induced EMF?

> The size of the area
The size of the magnetic field
The faster spinning of the coil (The greater the rate of change of magnetic flux, the greater the induced EMF)
The number of turns of the coil

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What is the equation for the induced EMF for a dynamo and what is its rearrangement?

> V = - dNBAcosθ/dt
V = -NBA d/dt(cosθ)
V = -NBA × -sin(θ)dθ/dt
V = NBAsinθ×dθ/dt
> V = NBAωsinθ 
> ω = 2π/t (angular frequency

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What are the equations for induced EMF for a dynamo: (4)

V = -dNBAcosθ/dt
V = NBAωsinθ
V = V0sin⁡(2πft)
V0 = 2πfNAB

What are the equations for magnetic flux for each coil in a transformer?

ϕp = NpAB
ϕs = NsAB

What is the equation relating the primary and secondary coil voltages?

Vp/Vs = Np/Ns

What is back EMF?

When a voltage is applied to a coil in a motor and the motor spins. there is a changing flux as the motor turns and this produces a voltage in the opposite direction to the applied voltage. Hence, the induced voltage counteracts the applied voltage.

What is the equation for the mechanical power of a wire placed in a magnetic field?

P = BILv
F = BILsinθ
Workdone: w = F∆x = Fv∆t
Power = ∆w/∆t = Fv
Power = BILv

When a wire is placed in a magnetic field and experiences a force and moves, an EMF is induced in it and so this has some power. What are the equations to model this?

Flux cut: ϕ = BA = BL∆x
Induced voltage: V = -BL.∆x/∆t = V = -BLv
Power: P = IV = -BLvI

How do mechanical power and induced EMF relate?

The equation for mechanical power developed and the induced power (from the induced EMF) is the same.
> Power = BILv

What is the equation to find the Electrical power of a wire in a magnetic field?

Electrical power = Mechanical power + Power dissapated
Vbatt × I = Vinduced × I + I^2R
Vbatt = Vinduced + IR

What is the equation to find the current in a wire in a magnetic field, knowing the Battery voltage and the back EMF?

``` I = (Vbatt - Vinduced) / R I = (Vbatt - Vbackemf) / R ```

How can the dissipated voltage and power be calculated?

Vbatt - Vbackemf = Dissipated voltage | Vbatt × I - Vbackemf × I = Dissipated power

What is the Permeability of free space and what is its value?

> This is the influence of a substance on the magnetic flux in the region it occupies. > 4π×10^-7

DO NOT MIX UP PERMEABILITY WITH PERMIATIVITY

BE CAREFUL

What is the equation used to calculate the magnetic field strength at a distance r from a wire?

B = μ0×I / 2πr | [BE AWARE DO NOT NEED TO LEARN]

What is the equation used to calculate the magnetic field coming up through the centre of a coil of wire radius r?

B = μ0NI/2r | [BE AWARE DO NOT NEED TO LEARN]

What are the equations used to calculate the magnetic field through a solenoid?

B = μ0NI/L n = Number of turns/Length B = μ0nI [BE AWARE DO NOT NEED TO LEARN, YOU WILL NEED TO APPLY IT]

What is the equation and constant when there is a material placed inside the solenoid?

B = μ0μrnI | Where μr is the permiability of the material inside the solenoid. This can help make the solenoid more magnetic

What is an inductor?

When placed in a circuit it and the circuit it turned on, a current starts to flow. An inductor opposes the change in the current and so it takes longer for the current to reach maximum because the quicker the current changes, the greater an opposing voltage is induced. This produces a rise time (the time it takes fro maximum current to be reached)

What is the equation for self inductance and what is its unit?

Symbol: L Unit: Henry (H) Constant for an inductor and dependent on the material within it.

What is the equation to calculate self inductance?

L = Back EMF from changing current / Rate of change of current

What is the equation to calculate the back EMF of an inductor?

Vback = LdI/dt

How can can self inductance be related to magnetic flux?

``` dϕ/dt = Ldi/dt ϕ = LI ```

Does a solenoid have a self inductance?

Yes

What is the equation to calculate the self inductance of a solenoid with a material in it?

``` ϕ = LI => L = ϕ/I L = NAB/I B = μ0μrnI => B = μ0μrNI/Length L = NA / I × μ0μrNI / Length L = μ0μrN^2A / Length [BE AWARE DO NOT NEED TO LEARN, YOU WILL NEED TO APPLY IT] ```

What is mutual inductance?

For two circuits next to each other, when one has a change in the current this will induce a voltage in the other circuit. Like a transformer.

What is the equation for mutual inductance for two circuits next to each other (circuit a and circuit b)?

M = ϕa / Ia = ϕb / Ib