7: Fields and Their Consequences Flashcards
What type of force is felt in a field?
-A non-contact force
Is a force a vector or a scalar?
-A vector
What are the similarities between the electrostatic force and the gravitational force?
-Both follow inverse square laws
-Both utilise field lines
-Both contain equipotentials
What are the differences between the electrostatic force and the gravitational force?
-Gravitational force is always attractive whereas electrostatic can also repel
-The electrostatic force is much stronger(by about 10^20)
Is the gravitational force attractive or repulsive?
-Attractive
How is the gravitational force at a point calculated?
-Force=(Gravitational constant * mass1 * mass2)/distance^2
-F=(G * M * m)/r^2
What is the definition of gravitational field strength?
-The force per unit mass
-g=F/m
How is the gravitational field strength at a point calculated?
-Field strength=(gravitational constant * mass)/distance^2
-g=(G * M)/r^2
What is gravitational potential?
-The gravitational potential energy per unit mass lost when moving a mass from infinity to a distance r from a body of mass M
What is gravitational potential energy?
-The gravitational potential energy lost when moving a mass from infinity to a distance r from a body of mass M
How is the work done in a gravitational field calculated?
-Work done=mass * change in potential
-ΔW=m * ΔV
-W=(G * M * m)/r
What is an equipotential surface?
-A surface in which no work is done moving an object between points on the equipotential surface
How is the gravitational potential at a point calculated?
-V=(G*M)/r
How is the orbital velocity calculated?
-Orbital velocity=√ ((Gravitational constant * Mass)/r)
-V=√ ((G * M)/r)
How is escape velocity calculated?
-Escape velocity=√ ((2 * Gravitational constant * Mass)/r)
-V=√ ((2 * G * M)/r)
How is the time period and radius of an orbit related?
-The time period squared is proportional to the radius cubed
-T^2 ∝ r^3
How do you calculate the electrostatic force at a point?
-F=(k *Q *q)/r^2
How do you calculate the electrostatic field strength at a point?
-F=(k*Q)/r^2
How do you calculate the electrostatic potential energy at a point?
-F=(k *Q *q)/r
How do you calculate the electrostatic potential at a point?
-F=(k*Q)/r
Where is the charge found in a charged sphere?
-At the centre of the sphere
What is the definition of electric field strength?
-The electrostatic force per unit charge
What is the definition of electric potential?
-The work done per unit charge moving a charge from infinity to a point
How are the field lines drawn for an electric field?
-Drawn in the direction that a positive charge would go
How are the field lines in a gravitational field drawn?
-Always towards the body of mass
How does a charged particle behave in a electric field?
-It’s motion is parabolic and can undergo circular motion
What is the definition of capacitance?
-The amount of charge stored for each 1 unit voltage across a set of plates
-C=Q/V
How is the capacitance of a dielectric calculated?
-C=(A *ε0 *εr)/d
Where:
A=area
ε0=permittivity of free space
εr=relative permittivity of the dielectric
d=distance between plates
How is the energy stored in a capacitor calculated?
-E=(1/2)QV=(1/2)CV^2=(1/2)*Q^2 /C
Where:
E=energy
Q=charge
V=voltage
C=capacitance
What are the equations for charging a capacitor?
-I0=Vs/R
-Vs=Vr+Vc
-I=I0 e^(-T/RC)
-Vr=Vs e^(-T/RC)
-Vc=Vs(1-e^(-T/RC))
-Q=Qf(1-e^(-T/RC))
What are the equations for discharging a capacitor?
-I0=V0/R
-Vr=Vc
-I=I0e^(-T/RC)
-Vr=V0e^(-T/RC)
-Vc=V0e^(-T/RC))
-Q=Q0e^(-T/RC))
What is the time constant for a capacitor equal to?
-The resistance multiplied by the capacitance
-T=RC
How long is the time to halve for a capacitor?
-0.69RC
What is the time constant for a capcitor?
-The time taken for the charge in a capacitor to fall to 37% of its initial value
How much charge is stored when charging a capacitor at each time constant?
-At 1RC: 63%
-At 3RC: 95%
-At 5RC: 99%
How much charge is left when discharging a capacitor at each time constant?
-At 1RC: 37% left
-At 3RC: 05% left
-At 5RC: 01% left
How does a capacitor charge up?
-Electrons move from negative to positive around the circuit
-The electrons are deposited on plate A, making it negatively charged
-Electrons travel from plate B to the positive terminal of the battery, giving the plate a positive charge
-Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates
-When the p.d across plates = source p.d., the capacitor is fully charged and current stops flowing
What factors affect the time taken for a capacitor to charge or discharge?
-The capacitance of the capacitor
-The resistance of the circuit
When does a magnetic field produce a force?
-When the field is perpendicular to the flow of current
How is the force on a current-carrying wire in a magnetic field calculated?
-Force=Flux Density *Current *Length of wire in field
-F=B *I *L
How is the force on a charged particle in a magnetic field calculated?
-Force=Flux density *charge *velocity
-F=B *Q *v
What is the definition of flux density?
-The force per unit length per unit current on a current-carrying conductor perpendicular to the field
What is the radius of a charged particle in a magnetic field?
-Radius=(mass *velocity)/(Flux density *charge)
-r=(mv)/(Bq)
What is magnetic flux?
-The perpendicular area which cuts a flux density
How is magnetic flux calculated?
-Magnetic flux=Flux density*area perpendicular
-Φ = BA
-Measured in Weber(Wb)
How is flux linkage calculated?
-Flux linkage=number of turns*magnetic flux
-ψ=NΦ
-Measured in Weber(Wb)
How is flux linkage calculated in a rotating coil?
-Flux linkage=Flux density *area *number of turns *angular velocity
-NΦ = BANcosθ = BANcos(ωt)
What is Faraday’s law?
-The conductor experiences a force due to the current
-This force opposes the motion of the conductor
-The induced emf is directly proportional to the rate of change of flux linkage
-emf=Number of turns*change in flux/change in time
-ε = (N ΔΦ)/Δt
What is Lenz’s law?
-The direction of the induced current is always such that it opposes the motion that created it
How is emf calculated for a rotating coil in a magnetic field?
-emf=Flux linkage *angular speed *sin(angular velocity)
-ε = BAN ω sin ωt
How is the maximum emf calculated for a rotating coil in a magnetic field?
-Max emf=Flux linkage*angular speed
-εMax = BANω
How is the root mean square voltage calculated?
-Vrms = V0/√2
How is the root mean square current calculated?
-Irms = I0/√2
What is the transformer equation?
Ns/Np = Vs/Vp
What is the efficiency of a transformer?
-Efficiency=(secondary current *secondary voltage)/(primary current *primary voltage)
How is power lost in transmission cables?
-Lost due to heating via I^2*R
What does Fleming’s left hand rule represent?
-The direction of the force felt by a current carrying conductor in a field
-Thumb: force
-Index: magnetic field
-Middle: current
How are the field lines in a magnetic field drawn?
-From north to south
How does a transformer work?
-A primary coil is wrapped around an iron core with an alternating p.d
-This creates an alternating magnetic field
-This magnetic field induces an EMF in a secondary coil also wrapped around the core.
-This creates a current in the secondary coil.
Why are transformers used?
-To be able to increase the voltage in transmission cables to minimise energy losses
-To decrease the voltage to ensure safe usage in households
What is an eddy current?
-The magnetic field of the primary coil induces an emf in the secondary coil
-This induces an emf in the secondary coil and induces min currents
-These currents are the eddy currents
How are eddy currents a problem?
-The eddy currents produced cause a field opposing the primary coil
-This causes energy loss via resistive heating of the iron core
-This reduce efficiency
How can energy losses via eddy currents be reduced?
-Use a laminated iron core
-Place an electrical insulator in between thin sheets of iron to reduce the eddy currents circuit
Information that can’t be put on flashcards
-Graphical representations of g and V against r for gravitational and electric fields
-Derivation of period^2 is proportional to the radius cubed
-Graphs for charge and discharge for a capcitor
