What happens when a conducting rod is moved perpendicularly through a magnetic field?
- The magnetic field will exert a force on the ‘free’ electrons in the rod, causing them to move [downwards]. Electrons accumulate at the top/bottom] of the rod, and an electric field is created between the two ends of the rod. Electrons stop moving once there is enough to repel new electrons.
How can you calculate the electric field created between the ends of a rod moving normally to a magnetic field?
- E = Ɛ/L
- Induced emf, Ɛ is the p.d. between the ends of the rod.
- L is the length of the rod
What is motional emf? How can you calculate it?
- The p.d. between the ends of a conducting rod length L moving at speed v normally to a magnetic field B.
- Ɛ = BvL
What are the ways to increase the current induced by moving a coil of wire through a magnetic field? [5]
- Increase the relative speed of the magnet and the coil
- Increase the strength of the magnet
- Increase the number of turns in the coil
- Increase the area of the loop
- Move the magnet at right angles to the plane of the loop.
What is magnetic flux? How can you calculate it?
Imagined as the number of field lines piercing a loop of wire in a magnetic field. Called flux linkage when there is more than one turn of wire.
- Φ = NBAcosθ (Weber - Wb)
N = Number of turns in coil
B = magnetic field strength
A = Area of the loop in the magnetic field.
θ = angle between the magnetic field and the normal to the loop area
What is Faraday’s law?
The induced emf (not necessarily current) of a coil in a magnetic field is equal to the negative rate of change of magnetic flux linkage.
- Ɛ = - NΔΦ/Δt
How can you work out motional emf of a rod in a magnetic field using Faraday’s law?
- Imagine the area swept out by the rod as L x vΔt
- Substitute this into the equation for change in magnetic flux. ΔΦ = BA
What is Lenz’s law?
- the induced emf will be in such a direction as to oppose the change in magnetic flux that created the current.
- (the magnetic field produced by the induced current must be in the opposite direction to the magnetic field creating the induced current - use RHG rule)
How does an ac generator work?
The ends of the coil are attached to slip rings which are in contact with carbon brushes. The flux in the coil changes as the coil rotates and so an emf is produced in it.
How can you calculate and graph the induced emf in an ac generator?
V = -ΔΦ/Δt = ωNBAsin(ωt)
Imagine a sine graph of voltage against time.
How can you calculate and graph the current produced by an ac generator?
- I = V₀sin(ωt)/R
V₀ is the peak voltage
ω is the angular speed of the coil
Imagine a sine graph of current against time
How can you calculate the power in an ac circuit?
P = V₀I₀sin²(ωt)
V₀ is the peak voltage
I₀ is the peak current
ω is the angular speed of rotation of the coil
∴ Pmax = V₀I₀
- Two oscillations on the graph corresponds to one rotation of the coil.
How can you find the average voltage, current and power in an ac circuit?
Use the root mean square (rms):
Irms = I₀/(√ 2)
Vrms = V₀/(√ 2)
P[bar] = V₀I₀/2 = IrmsVrms
How can ac current be converted to dc current?
- Using a single diode (half wave rectification. Graph turns into a series of flats and hills. Has the disadvantage that half the power is lost.
- Using a diamond of diodes all pointing in the sameish direction, with two circuits connected to opposite corners of the diamond. Graph is a series of hills.
What is capacitance?
The charge per unit voltage that can be stored on a capacitor (a property of the capacitor): C = q/V = εA/d (F)
q = the charge on one of the plates
V is the potential difference between the plates
ε is the permittivity of the medium between the plates
A is the area of overlap
d is the plate separation
What is a dielectric? How does it work?
- It is an insulator inserted between the plates of a capacitor to increase its capacitance.
- The electric field created between the plates of the capacitor exerts a force on the charges of the dielectric, causing charge polarization. This creates a small electric field within the dielectric, reducing the net electric field between the plates.
How can you work out the total capacitance of two or more capacitors connected in parallel?
Add the individual capacitors together:
Cparallel = C₁ + C₂ …
How can you work out the total capacitance of two or more capacitors in series?
1/Cseries = 1/C₁ +1/C₂ …
How can you calculate the energy stored in the electric field between the plates of a capacitor?
Find the area under a p.d. vs charge stored graph.
E = (1/2)CV²
E is the energy stored
C is the capacitance
V is the p.d. between the plates
Substitute quantities using C = q/V for more equations.
What is a circuit set-up for charging a capacitor?
Use a two way switch that can connect the capacitor to two circuits.
What does the graph look like for a charging capacitor?
- p.d or charge against time
- current against time
- A curve passing through the origin that gradually flattens off. The p.d. or charge increases until V = Ɛ emf of the battery and q = CƐ
- A curve that tends to zero, starting at I₀ = Ɛ/R
What is the time constant (for a capacitor)?
τ = RC = resistance x capacitance
The time constant is the time after which the charge on a discharging capacitor decreases to about 37% of its initial value.
the time constant is the time needed for the charge to decrease to half its initial value, divided by ln 2
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How can you smoothen the rectified output dc current from an ac input?
Put a capacitor in parallel to the load. As the voltage increases, the capacitor stores charge. As the voltage decreases, the capacitor discharges, sending current through the load, and ‘smoothening/flattening’ the voltage time graph.
