7. Electric and Magnetic Fields Flashcards
What is a force field?
An area in which an object experiences a non-contact force.
How can force fields be represented?
- Vectors.
- Field lines.
What is an electric field?
A force field in which a charged particle experiences a force.
What is the electric field strength?
The force per unit charge experienced by an object in an electric field.
Given by the formula E = F/Q
What is the difference between the electric field strength of uniform fields and radial fields?
In uniform fields the value of the electric field strength is constant.
In a radial field, it varies.
What does coulombs law state?
F = (Q₁Q₂) / 4πε₀r²
The magnitude of the force between two point charges is:
- directly proportional to the product of their charges.
- inversely proportional to the square of the distance between them.
what is ε₀ and r in:
F = (Q₁Q₂) / 4πε₀r²
ε₀ is the permittivity of free space.
r is the distance between charges (from their centres).
What happens if F is negative in coulombs law?
F = (Q₁Q₂) / 4πε₀r²
The force is attractive if F is negative.
The fore is repulsive if F is positive.
When do you use this equation?
E = Q/4πε₀r²
To find the electric field strength of a point charge forming a radial field.
What is the absolute electric potential (V)?
The potential energy per unit charge of a positive point charge at a point in the field.
How does the absolute magnitude of electric potential change in a radial field?
- It is greatest at the surface of the charge.
- as the distance from the charge increases, its potential decreases.
- Its electric potential at infinity is 0.
What happens to the potential and polarity if the sign of the charge is positive/negative?
If a charge is positive…
- its potential is positive.
- its charge is repulsive.
If a charge is negative…
- its potential is negative.
- its charge is attractive.
What does V-r look like for a repulsive charge?
What does V-r look like for an attractive charge?
(V = electric potential) (r = distance from centre of charge)
Repulsive:
- As V decreases, r increases at a growing rate.
- V is initially positive.
Attractive:
- As V increases, r increases at a growing rate.
- V is initially negative.
When do you use this equation?
E = V/d
To find the electric field strength in a uniform electric field.
How can you form a uniform electric field?
Using parallel plates with a potential difference across them.
What is electric potential difference?
The energy needed to move a unit charge between two points.
What do field lines show?
in an electric field
The direction of the force acting on a positive charge.
What does the distance between field lines represent?
The magnitude of force.
What do equipotential lines show?
The points where the potential in a field are the same.
- When a charge moves along an equipotential line, no work is done.
What is capacitance?
The charge stored by a capacitor per unit potential difference.
What is the area under a graph of charge against potential difference for a capacitor?
The electrical energy stored by a capacitor (W).
Describe the graph of charge against potential difference for a capacitor?
A straight line through the origin.
as potential difference is directly proportional to charge
When charging a capacitor, what do the graph of:
I-t
V-t
Q-t
…look like?
I-t
decreasing slope
(are under = charge)
V-t
Increasing slope
Q-t
Increaing slope
(gradient =current)
describe what happens when you charge a capacitor to explain the graphs of I-t, V-t and Q-t?
Once a capacitor is connected to a power supply…
- current starts to flow and negative charge builds up on the plate connected to the negative terminal.
- On the opposite plate, electrons are repelled by the negative charge building upon the initial plate.
- Therefore electrons move from the positive terminal and an equal but opposite charge is formed on each plate.
- This creates a potential difference across the plate.
- As the charge across the plate increases, the potential difference increases but the electron flow decreases.
- This is due to the electrostatic repulsion also increasing.
- Therefore the current decreases — eventually to zero.
When discharging a capacitor, what do the graph of:
I-t
V-t
Q-t
…look like?
I-t
decreasing slope
(are under = charge)
V-t
decreasing slope
Q-t
decreasing slope
(gradient =current)
Why are the discharging graphs of I-t, V-t, Q-t the way they are?
When the capacitor is dischargin…
- the current flows in the opposite direction.
- and the current charge and potential difference across the capacitor falls exponentially
- They take the same amount of time for each value to half.
What is the time constant when talking about capacitors?
- RC
- it is the time taken for it to discharge to 1/e (0.37) of its initial value (of charge, current and voltage)
- it is the time taken for it to charge to 1 - 1/e (0.63) of its maximum value (of charge or voltage)
How do you find the time constant for a capacitor from a graph?
IF the graph is decreasing, find the time at y = 0.37
ELSE IF the graph is increasing, find the time at y = 0.63
How would you plot Q = Q₀e⁻ᵗ/ᴿᶜ in the form y = mx + c
Q = Q₀e⁻ᵗ/ᴿᶜ
ln(Q) = ln(Q₀e⁻ᵗ/ᴿᶜ) ln(Q) = ln(Q₀) + ln(e⁻ᵗ/ᴿᶜ) ln(Q) = ln(Q₀) - t/RC
ln(Q) = -1/RC(t) + ln(Q₀)
y=m(x) + C
plot ln(Q) angaint t
Derive V = V₀e⁻ᵗ/ᴿᶜ and I = I₀e⁻ᵗ/ᴿᶜ from Q = Q₀e⁻ᵗ/ᴿᶜ.
Q = Q₀e⁻ᵗ/ᴿᶜ C = Q/V ∴ Q=CV
Q₀=CV₀
CV = CV₀e⁻ᵗ/ᴿᶜ
V = V₀e⁻ᵗ/ᴿᶜ
V=IR
V₀=I₀R
IR = I₀Re⁻ᵗ/ᴿᶜ I = I₀e⁻ᵗ/ᴿᶜ
What is the magnetic flux density of a magnetic field?
- A measure of the strength of the field.
- Measured in Tesla.
What is magnetic flux?
Symbol: Φ
describes the magnetic field or magnetic field lines passing through a given area.
How do you work out magnetic flux when the field is perpendicular to the area?
Φ = BA
B is the magnetic flux density
A is the area
What is magnetic flux linkage?
Symbol: NΦ
it’s the magnetic flux multiplied by the number of turns.
Why does a current-carrying wire experience a force in a magnetic field?
- it has electrons that are charged and so a force acts of them in a magnetic field.
- A particle has a force of magnitude BQvSinθ
- The wire has a force of magnitude BIlSinθ.
Describe electromagnetic induction?
- A conducting rod/bar magnet moves relative to a magnetic field/a coil of wire.
- It experiences a rate of change of flux linkage.
- This causes an equal magnitude of emf to be induced in the rod. (Faraday’s Law)
- If the coil of wire forms a complete circuit, a current is induced which opposes the motion causing it.(Lenz’s Law)
What factors affect the emf induced in a coil during electromagnetic induction?
- The number of turns: directly proportional (due to Faraday’s law).
- The magnetic flux density: directly proportional (as Φ = BA).
- The cross-sectional area of coil: directly proportional (as Φ = BA).
- Time taken for motion: inversely proportional (due to Faraday’s law).
Describe electromagnetic induction in transformers?
- The primary coil carries an alternating current.
- The current-carrying wire creates a changing magnetic field in the iron core.
- The rate of change of flux linkage across the second wire induces an emf in the coil. (due to Faraday’s law).
- because the coil is in a closed circuit a current is also induced. This acts in the opposing direction to the current in the primary coil (due to Lenz’s law).
What factors affect the emf induced in the secondary coil of a transformer?
The magnetic flux density created by the initial coil:
- directly proportional.
- determined by the number of turns (l) and the current (I) flowing through the wire.
The distance between the two coils:
- inversely proportional.
- as the further they are, the less magnetic flux passes through the second coil and so the induced emf is lower.
The number of turns in the second coil:
- directly proportional.
The cross-sectional area of the second coil:
- directly proportional.
The frequency of alternating current:
- directly proportional.
- dependent on the time take for the current to change.
How does a magnet falling through a coil demonstrate Lenz’s law?
- As the magnet approaches the coil, there is a rate of change of flux linkage through the coil, so an emf and currents are induced.
- The direction of the current opposes the motion of the magnet, so the same pole as the pole the magnet approaching the coil will be induced in order to repel it.
- This causes the magnet to slow down due to the force of repulsion.
- As the magnet passes through the centre of the coil there is no change in flux linkage so no emf is induced.
- As the magnet leaves the coil the is a rate of change of flux linkage, so en emf and current are induced that opposes the motion of the magnet.
- Thus an opposing pole is induced by the agent causing it to slow down once again, due to the force of attraction.
Why is UK voltage given as 230V if it peaks at 330V?
230V is the root mean squared.
330/√2 ≈ 230V
