Electric and Magnetic Fields Flashcards
What is an electric field
A region in which a charged particle experiences a non-contact force, attraction or repulsion. Like a force field.
What is electric charge measured in
Coulombs
What happens when a charged object is placed in an electric field
The object will experience a force
If the charged object is a uniformly charged sphere, what do you assume
Assume all of its charge is at its centre, it behaves like a point charge with a radial field.
How are electric fields represented
With field lines
What does coulombs law tell you
The force of attraction or repulsion between 2 point charges in a vacuum.
What is coulombs law
F = Q1Q2/4piE_0r^2
What is the relationship between Q1 and Q2 in coulombs law
The FORCE on Q1is always equal and opposite to the force on Q2, the direction of the force depends on the charges. This means regardless of their attraction, the force on Q1 and Q2 will always be equal and opposite
What happens to force between charged particles as they get further apart
Coulombs law is an inverse square law, the further apart the charges, the weaker the force between them.
What happens to Coulombs law if the particles are not in a vacuum
E_0, permittivity in vacuum, is replaces by E, permittivity of the material they are in. Air is treated as a vacuum.
How do you treat the permittivity of air when using coulombs law
Permittivity of air is same as permittivity in vacuum. Keep it as E_0
How do you experimentally measure the force between 2 charges
Use an electronic balance. Fix a charged sphere to a mass balance and zero the balance. Clamp another charged sphere carrying the same charge directly above the first sphere (make sure the 2 don’t touch). The spheres will repel each other, causing the lower sphere to push down on the scale, so the scales will register a mass. Convert mass reading on the scales into a force using F=W=mg
If you vary the distance between spheres, r, then you should find F is directly proportional to 1/r^2
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How do you charge spheres in the experiment to find force between 2 charges
By connecting the spheres to a power supply
What is electric field strength, E
Force per unit positive charge. The force that a charge of +1C would experience if placed in the electric field.
What is the equation for electric field strength
E = F/Q
What are the units for electric field strength
N C^-1
How does electric field strength vary in a radial field and in a uniform field
In a radial field, electric field strength depends on where you are in the field. In uniform field, electric field strength is the same everywhere
What direction is electric field strength pointing in
Electric field strength is a vector pointing in the direction that a positive charge would move
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What type of field does a point charge have
Radial field
Where is electric field the strongest in a radial field
The area where the field lines are closest together, highest field line density area
Which direction would the field lines on a radial field point for a negatively charged particle
Point towards the particle. Field lines point in the direction a proton would travel, and protons are attracted to negative charge, so they would go towards negative charge.
Which direction would the field lines on a radial field point for a positively charged particle
Away from the particle
What does the electric field strength depend on in a radial field
The distance from the point charge and magnitude of charge on point charge
How does electric field strength decrease as you get further away from the point charge in a radial field
Inverse squarely. E is inversely proportional to r^2. The further away the field lines are from each other, the weaker the electric field strength on a radial field.
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How is a uniform electric field produced
By connecting 2 parallel plates to the opposite poles of a battery
How are the field lines drawn in a uniform electric field
The field lines are parallel to each other and point from the positive plate to the negative plate
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How far apart are the field lines in a uniform electric field
They are the same distance apart from each other, equidistant. This means the field strength is the same everywhere in the field.
What does the electric field strength depend on in a uniform electric field
The potential difference between parallel plates, and the distance between the plates.
What is the equation for electric field strength of a uniform electric field
E = V/d
E is measured in Vm^-1
PRAC, how do you investigate charged drops in a uniform electric field
An atomiser creates a fine mist of oil drops that are charged by friction as they leave the atomiser. When the circuit is witched off, a drop falls from the top plate to the bottom plate due to its weiht. When the circuit is switched on, the pd between the plates creates a uniform electrci field, which exerts a force on the oil drop. A negatively charged oil drop can be made to float between the plates bu balancing the upaward fromce from the electric field with the downaward force of the oil drops weight by adjusting the voiltage between plates.
EQUATIONS
If you increase the pd while a drop is floating between plates, i.e the forces on the drop are balanced, you increase field stregnth. This means the forces on the oil willno longer be balanced so it will accelerate towards the positive top p;ate because the force due to the electric field is greater than its weight. If you increase the distance between the plates or decrease the pd, you reduce the field strength and therefore the electric force on the oil drop. The oil drop will acceleerate towards the bottom due to its weight being larger than the force due to the electric field.
If theres no electric field, the drop will accelerate until it reaches terminal velocity, when drag = weight of the drop
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What is an electric potential
The electric potential (voltage) a particle with +1C would have at a specific point in an electric field.
What does electric potential of a point depend on
How far it is from the charge, and the size/magnitude of the charge
What is the equation for electric potentials IN A RADIAL FIELD
V = Q/4piE_0r
V - electric potential (V)
Q - size of charge (C)
r - distance from charge (m)
What does the sign of V depend on in an electric potential
The sign of Q. If Q is positive, the force is repulsive and V is positive. If Q is negative, the force is attractive, and V is negative.
How does V change in electric potentials as you get further away from the point charge
Magnitude of V is greatest directly next to the charge, and decreases as the distance from the charge increases. V will be zero at an infinite distance from the charge.
What do the graphs of V against r look like for repulsive and attractive forces, for electric potentials
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Repulsive force, V is initially positive and tends towards zero as r increases towards infinity
Attractive force, V is initially negative and tends to zero as r increases towards infinity.
What does the gradient of a tangent of a V against r graph tell you, V being electric potential
Field strength at that point. E = ΔV/Δr
How can you find ΔV (change in electric potential) from a graph of E, electric field strength, against r, distance from charge, between 2 points. Change in electric potential between 2 points
Find the area under the graph between your 2 chosen points
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What is an equipotential
A line highlighting the area where the electric potential is equal.
What do equipotentials look like in radial fields
Wherever the radius of 2 points is equal, that is where the equipotential is. Both points have to be the same distance from the centre to have the same electric potential
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What do equipotentials look like in uniform fields
They are flat planes perpendicular to the direction of travel by charge. For example, each area that is within the +200V range between the 2 parallel plates will have the same electric potential.
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How does charge move along an equipotential
No work is done when you are traveling along an equipotential. An electric charge can travel along an equipotential without any energy being transferred.
What does a capacitor do
Store electrical charge
How are capacitors made
Two conducting plates separated by an air gap or insulating material.
What is the circuit symbol for capacitor
–||–
How does a capacitor work
When a capacitor is connected to a power source, positive and negative charge builds up on opposite plates. The insulating material stops charge moving between the 2 plates so a potential difference is created. This creates a uniform electric field between plates.
What is the unit to measure charge stored by a capacitor
Capacitance, the charge per unit voltage stored by a capacitor
What is the equation for capacitance, and units
C = Q/V
C is measured in Farads, F. Usually expressed as microfarads or nanofarads
Q - Coulombs
V - Voltage
What are farads usually expressed as in size
Farad is a huge unit, so capacitance is often in microfarads or nanofarads.
How does a capacitor work in a circuit
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When the switch is flicked to the left, and the circuit is split up, charge builds up on the plates of the capacitor. Electrical energy provided by the battery is stored by the capacitor. If the switch is flicked right, and the circuit is connected, the charge stored on the plates will discharge from the capacitor to the light bulb. Electrical energy turns to heat and light energy.
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Why is some energy lost when charging the capacitor
Work is done removing negative charge from one plate and depositing it onto the other plate to charge the capacitor. This comes from the electrical energy of the battery. This is given by
charge x average p.d
How do you find work done in a Voltage against Charge graph
You can find energy stored from the area under a graph of p.d against charge stored IN CAPACITOR
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p.d across capacitor and charge stored on capacitor is proportional to each other, so the graph will be a straight line through the origin. The energy stored is given by the yellow triangle
What is energy stored on capacitor equal to
Energy stored by capacitor is equal to work done
What is the equation for energy stored by capacitor
W = 1/2 QV
What are the other 2 forms of W = 1/2 QV
W = 1/2 CV^2
W = 1/2 Q^2/C
These are done by substituting variations of C = Q/V into the original equation. Q = CV for the top one, V = Q/C for the bottom one
How do you investigate what happens when you charge a capacitor
Set up circuit, close switch and connect uncharged capacitor to power supply, let capacitor charge while data logger records p.d (from voltmeter) and current (from ammeter) over time. When current through ammeter is 0, capacitor is fully charged. You can use a computer to plot a graph of charge, p.d or current against time.
How do you know when a capacitor is fully charged in the experiment investigating what happens when you charge a capacitor
When the current on the ammeter is 0, capacitor is fully charged. This is also when the p.d across the capacitor is equal to the p.d across the power supply.
How do you generate a graph of Charge over time, Q-t graph, when you only have readings for current, voltage and time in the experiment where you charge a capacitor
ΔQ = IΔt. Charge transferred in a given time is equal to the area under the I-t graph up to that point. This is how you generate the Q-t graph
What is Q_0, V_0, I_0 in capacitor graphs
Q_0 - The charge on the capacitor when its fully charged,
V_0 - the potential difference across the capacitor when its fully charged
I_0 - the maximum current flowing through the circuit
How do you set up the circuit in the investigation where you charge a capacitor
How do you explain the shape of the Q-t graph for the investigation of what happens when you charge a capacitor
As soon as switch is closed, current starts to flow. The electrons flow onto the plate connected to the negative terminal of the power supply, so a negative charge builds up. The build up of negative charge repels electrons off the plate connected to the positive terminal of the power supply, making that plate positive. Electrons are attracted to the positive side.
How do you explain the shape of the V-t graph for the investigation of what happens when you charge a capacitor
An equal but opposite charge builds on each plate, causing a p.d between plates. No charge can flow between plates because they are separated by an insulator
How do you explain the shape of the I-t graph for the investigation of what happens when you charge a capacitor
Initially the current through the circuit is high. At the start, the CURRENT IS HIGH. But as charge builds up on the plates, electrostatic repulsion makes it harder and harder for more electrons to be deposited. When p.d across capacitor is equal to p.d across the power supply, the current falls to 0. Capacitor is fully charged.
What happens to charge, potential difference, and current as a capacitor is charged
Charge increases, potential difference increases, current decreases
How do you discharge a capacitor
Remove the power supply and close the switch.
You take away it’s source of power, then open the flood gates.
How do you know when a capacitor is fully discharged
When current through the ammeter and p.d across plates are both 0, the capacitor is fully discharged
In the experiment where you charge a capacitor, what should you do once you have recorded all the readings for a capacitor charging up to it being fully charged
Let the capacitor discharge whilst the datalogger records potential difference and current over time.
What happens to current, charge and p.d as the capacitor discharges
Current decreases, charge decreases, p.d decreases
Why does current decrease as a capacitor discharges
Current flows in the opposite direction as charging current. As p.d decreases, the current decrreases as well.
Which direction does current flow when a capacitor discharges
The opposite direction as the charging current.
How long does it take for current, charge and p.d to fall as a capacitor is discharging and why
When a capacitor is discharging, the amount of charge on plates and p.d between plates falls exponentially with time. That means it always takes the same length of time for the charge or p.d to halve, no matter what value it starts at. Like radioactive decay. Same is true for amount of current flowing around the circuit.
How does an oscilloscope work
Basically, screen is divided into divisions. Y-axis is volts, x-axis is seconds. You use Gain to adjust scale of y-axis and timebase to adjust scale of x-axis. This helps you read measurements easier.
The screen of an oscilloscope is split into squares called divisions. Vertical axis is in volts. Volts per division shown on this axis is controlled by gain dial. This is the scale of the y-axis. The horizontal axis is in seconds. Seconds per division controlled by timebase dial. (scale of x-axis). Time base can be turned on and off. You can alter gain and timebase to make it easy to read off measurements. There’s also a button to freeze whatever’s on screen.
What can you use instead of a data logger and voltmeter to measure and record p.d across capacitor over time
CRO, cathode ray oscilloscope
What do you get when you turn the timebase off, on an oscilloscope when you connect it across a charging capacitor
You just get a dot in the middle of the display which tells you the p.d across the capacitor. If you take regular readings of this p.d for a charging and discharging capacitor, you can plot V-t graphs
What do you get when you turn the timebase on, on an oscilloscope when you connect it across a charging capacitor
If you turn timebase on and adjust the dial to fiddle with the resolution, you can get the oscilloscope to plot the voltage-time graphs for you on the display. Once capacitor is fully charged, you can press stop (freeze) button and copy the information from the display.
What is the analogy for charging and discharging a capacitor
Think of when you pump a bike tire. When there is no air in it, you can pump it easily, the air goes in easily. As more and more air fills the tire, the pressure increases, making it harder for you to pump it. The tire is full when the pressure of the air in the tire equals the pressure of air in the pump. Same analogy works for discharging as well.
What does the time taken to charge or discharge a capacitor depend on
- The capacitance of the capactitor (C). This affects the amount of charge that can be transferred at a given p.d
- The resistance of the circuit (R). This affects the current in the circuit
What is the equation to calculate the charge left on the plates after a capacitor begins discharging from being fully charged.
The equation for the charge graph.
What are the equations of voltage and current in a discharging capacitor
What is the time constant, 𝜏
The time taken for the charge, p.d or current of a discharging capacitor to fall to 37% of its value when fully charged. It is also the value of the charge or p.d, not current for charging capacitor, of a charging capacitor to rise to 63
Why is the time constant, 𝜏, so specific at 37%
If you take the value of time as 𝜏, which 𝜏=RC and put it into the p.d, current or charge equations of a dicharging capacitor, you get an answer of 1/e. 𝜏 is basically the value of t which will turn the power of e to -1.
What is the 𝜏 also written as
𝜏=RC
R - Resistance
C - Capacitance
How does a larger resistance and larger capacitance affect the time it takes for a capacitor to charge or discharge
the larger the resistance in series with the capacitor, and the higher the capacitance, the longer it takes to charge or discharge
How long does it normally take for a capacitor to charge or discharge fully
About 5 RC
How much time does it take for the charge, current, or p.d in any given RC circuit to halve, T_1/2
0.69 RC
Why does it take the same amount of time for the current, p.d, or charge to halve in any RC circuit
Because the charge, current and p.d fall exponentially with time for a discharging capacitor, so it takes the same length of time for any of these 3 values to halve no matter what values they start with.
How do you find the time constant with log-linear graphs
Rearrange any discharging capacitor equation by taking natural logs (ln) of both sides and rearranging. You get an equation in the form of y=mx+c, so plot that graph of lnQ against time. To get time constant from the graph, divide -1 by the gradient of the line.
For the graph of ln(Q) against time for a discharging capacitor, what is the value of the gradient and the y-intercept
Gradient: -1/RC or -1/𝜏
y-intercept: ln(Q_0)
How do you rearrange the equation of charge for a discharging capacitor to find time constant through log-linear graphs
Take natural logs of both sides then rearrange
How do you get the value for the time constant once you have plotted a log-linear graph for charge on a discharging capacitor
Divide -1 by the gradient of the line. This works because the gradient is -1/RC
Which equations do you use to plot log-linear graphs for current and p.d of a discharging capacitor
What is the difference in the log-linear graphs for current, p.d, and charge of a discharging capacitor
The y-intercept will equal I_0, Q_0, and V_0 respectively. That is the only change. The gradient for all of the graphs is still -1/RC
What is a magnetic field
A field or region where force is exerted on magnetic materials
How are magnetic fields represented
With field lines, also called flux lines
How do magnetic field lines work
They go from the north to the south pole of a magnet. The closer the lines are, the stronger the field.
What do field lines around a bar magnet, and between 2 bar mangets with N N and N S look like
Why is a magnetic field induced around a wire
When current flows in a wire, or any other long straight conductor, a magnetic field is induced around it. A current induces a magnetic field
What do field lines around a wire look like
Concentric circles centred on the wire. This is the wire if you looked at it from a 2-D plane. Just the top circle of the cylinder
How can you work out the direction of a magnetic field around a current-carrying wire
With the right hand rule
How do you use the right hand rule
Make a thumbs up with your right hand. The thumb shows you the direction of conventional current. People are conventionally right handed and you are currently holding your right thumb up because life is good. And the direction which your other fingers are curling is the direction of the field. The 3 fingers look like a sideways ‘m’ for magnetic field.
How do you use the right hand rule
Make a thumbs up with your right hand. The thumb shows you the direction of conventional current. People are conventionally right handed and you are currently holding your right thumb up because life is good. And the direction which your other fingers are curling is the direction of the field. The 3 fingers look like a sideways ‘m’ for magnetic field.
What is the magnetic field shape of a wire in a coil shape, and the magnetic field of a solenoid, a long spring of wire
What direction does conventional current flow
POSITIVE to NEGATIVE. You are having a positive day until you get shocked, then you have a negative day.
What will happen to a wire carrying a current when put in a magnetic field
It will experience a force
What happens to the magnetic fields when you put a current carrying wire between 2 magnets (an external magnetic field)
The field around the wire and the field from the magnets are added together. This causes a resultant field – the lines closer together show where the magnetic field is stronger. The bunched lines cause a ‘pushing’ force on the wire.
How do you use flemings left hand rule to find the relationship between field, force, and current
First finger Field. SeCond finger Current. ThuMb is the direction of motion, which is the direction of force.
What is the relationship between force, current direction and magnetic field
The force is always perpendicular to both the current direction and the magnetic field
What happens if the current direction is parallel to the magnetic field lines
Then the size of the force is 0N. There is no component of magnetic field perpendicular to the current.
What is force on a wire proportional to
Flux density. The force on a current-carrying wire at a right angle to an external magnetic field is proportional to the magnetic flux density, B.
What is magnetic flux density also known as
Magnetic field strength
What is the definition and symbol for magnetic flux density
Magnetic flux density, B, is the force on one meter of wire carrying a current of one amp at right angles to the magnetic field
Why is magnetic field strength also known as magnetic flux density
The magnetic field is strongest where the flux lines are closest together. So higher flux density means a stronger magnetic field
What is the equation linking force and flux density
F = BIℓ
F - Force (N)
B - Flux Density (T)
I - Current (A)
L - length of wire (m)
What is flux density measured in and is it a scalar or vector
Flux density is a vector with both direction and magnitued. Measured in teslas, T. Usually given in militesla, mT.
When is the force on a current-carrying wire greatest in a magnetic field
When the wire and the field are perpendicular
How does force on a wire change in a magnetic field as you change the angle of the wire
q
The more perpendicular the wire to the magnetic field, the larger the force it will experience. The more parallel, the less force it will experience.
What happens when the wire and the magnetic field are parallel
The wire experiences no force
What is the equation linking the angle between the wire, magnetic field, and flux density
F = BIℓ sinθ
Which component of magnetic field causes a current-carrying wire to experience a force
The force on a current-carrying wire in an external magnetic field is caused by the component of magnetic field perpendicular to the wire – Bsinθ
Does F = BIℓ sinθ apply to only current-carrying wires
No, it applies to any current-carrying conductor
Why do current carrying wires experience force in a magnetic field
Electric current in a wire is the flow of negatively charged electrons. Forces act on charged particles moving in a magnetic field. This is why current-carrying wires experience force in a magnetic field.
What is the equation to find the force acting on a moving charged particle in a magnetic field
F = Bqv sinθ
F = force (N)
B = flux density (T)
q = charge on particle (C)
v = velocity of particle (ms^-1)
θ = angle between current and field linesv
What direction is the force on a moving charge in a magnetic field, and what is this used for
The force on a moving charge in a magnetic field is always perpendicular to its direction of travel. This is the condition for circular motion. This effect is used in particle accelerators.
What should you think of magnetic flux density as
Total number of field lines per unit area
W
What is magnetic flux
Think of it like the total number of field lines
What is the equation for magnetic flux, and the units
Φ = BA
Φ - Flux (Wb)
B - Flux density (T)
A - Area (m^2)
What happens when a conductor cuts through magnetic flux
An emf is induced within the conductor
How does a conductor cutting through magnetic flux induce emf
If there is relative motion between a conducting rod and a magnetic field, the electrons in the rod will experience a force, causing them to accumulate at one end of the rod. This induces an electromotive force (emf) across the ends of the rod.
What is it called when a conductor passes through magnetic flux and induces emf
Electromagnetic induction
What is it called when a conductor passes through magnetic flux and induces emf
Electromagnetic induction
When is emf induced in electromagnetic induction
When the flux lines are broken. Whenever the magnetic field (or magnetic flux) that passes through a conductor changes
How is an emf induced in a solenoid or flat coil
When the move the magnet towards or away from the coil, or when you move the coil towards or away from the poles of the magnet.
What happens when you change the direction you are moving the magnet through a solenoid
The change in direction will mean the change in voltage. If moving forward for example, a positive emf may be induced, but moving it backward induces a negative emf
What does more turns in a coil of wire or solenoid mean in electromagnetic induction
More turns in coil of wire means bigger emf will be induced
What factors affect the size of emf induced in magnetic flux
The magnetic flux passing through the coil, Φ, and the number of turns in the coil that cut the flux, N
What is flux linkage
The product of the flux passing through a coil and the number of turns in the coil that cut the flux
What is the equation for flux linkage
NΦ = BAN
B - Magnetic Flux Density
A - Current
What does the rate of change in flux linkage tell you
How strong the electromotive force will be in volt. This is the rate of change of flux thing Mr. Richardson keeps telling us about. The higher the rate of change of flux linkage, the stronger the voltage or emf will be.
What will a change in flux linkage induce in terms of emf
A change in flux linkage of one weber per second will induce an electromotive force of 1 volt in a loop of wire.
What is the units of flux linkage and flux, Φ
Weber turns. Wb. This is the unit for both flux linkage and Φ.
What should you do if the magnetic flux isn’t perpendicular to the area you are interested in
Resolve the magnetic field into parallel and perpendicular vectors. That way you can only consider the perpendicular component.
What is the equation to find magnetic flux for a single loop of wire when B is not perpendicular to the plane of the loop.
For a single loop of wire, when B is not perpendicular to the plane of the loop, you can find the magnetic flux using equation:
Φ = BA cosθ
θ is the angle between the field and the normal to the plane of the loop. cosθ is the perpendicular component of the magnetic field.
What is the equation for flux linkage when the magnetic field is not perpendicular to the area you are interested in
NΦ = BAN cosθ
θ is the angle between the field and the normal to the plane of the loop. cosθ is the perpendicular component of the magnetic field
You simply add the cosθ to the equation which you use normally with perpendicular magnetic field.
What is proportional to the induced emf in electromagnetic induction
The induced emf is directly proportional to the rate of change of flux linkage. This is called Faraday’s Law
How do you write ‘emf is directly proportional to rate of change of flux linkage’ in an equation
ε = flux linkage change/time taken = d(NΦ)/dt
ε = d(NΦ)/dt
ε is magnitude of induced emf, N = 1 if it is just a single loop
What does ε = d(NΦ)/dt not give you
The direction of the emf. This equation only gives you the magnitude
How do you get change in flux linkage from an emf against time graph
Take the area under the graph
How do you get the emf from a flux linkage against time graph
Take the gradient of the graph. Remember emf is also rate of change of flux over time.
How do you get the emf from a flux linkage against time graph
Take the gradient of the graph. Remember emf is also rate of change of flux over time.
What is Len’s Law
The induced emf is always in such a direction as to oppose the change that caused it. So a magnet must be pushed through a solenoid which will provide some resistance for an emf to be induced
Why is there resistance when you push a magnet through a solenoid or a coil
The conservation of energy law. The energy used to pull a conductor through a magnetic field, against the resistance caused by magnetic attraction/repulsion, is what produces the induced current. Work has to be done for energy to be induced.
How do you link Lenz’s Law and Faraday’s Law to give you an equation which tells you the direction and the magnitude of emf
ε =-flux linkage change/time taken = -d(NΦ)/dt
ε = -d(NΦ)/dt
the minus sign shows the direction of the induced emf
What can Lenz’s Law help you find
Lenz’s Law can be used to find the direction of an induced emf and current in a conductor travelling at right angles to a magnetic field, perpendicularly to a magnetic field
How do yoyu find the direction of the current/induced emf in electromagnetic induction
Lenz’s Law says induced emf will produce a force to oppose the motion of the conductor, a resistance. Use Fleming’s left hand rule and point your thumb in the direction of the resistance, so opposite direction of conductors motion. And then point your first finger in the direction of the magnetic field. Your second finger will give you direction of the induced emf, or if conductor is part of a circuit, a current will be induced in the same direction as the induced emf.
What is alternating current
Alternating current or voltage is one that changes direction with time. The voltage across a resistance goes up and down in a regular pattern. It alternates between positive and negative in the shape of a sine wave.
What is an alternator
A generator of alternating current
How does a generator work
Generators, or dynamos, convert kinetic energy into electrical energy. They induce an electric current by rotating a coil in a magnetic field. The diagram shows a simple alternator, a generator of a.c. It has slip rings and brushes to connect the coil to an external circuit. fuck this stupid shit bruv.
