Electromagnetism and Electricity
Electric Force, Strength and Potential
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ℚ1ℚ2
Coulomb’s inverse square law is F = 4πℇ ∂r where F is a vector quantity
1
4πℇ ∂
is called the constant of proportionality and has a value of 9x109 Nm2C-2.
When there are 3 points the resultant force must be found using trigometry
An electrical field is said to be present at a point if a force of electrical origin is exerted on a charge placed at
that point
The electrical field strength is the electrical force acting on unit positive charge placed at that point, it has
F
Q
equations E = ℚ and E = 4πℇ ∂r2
If two points are repulsed then subtract the field strength to find the total, if they are attracted add the field
strengths to find the total
The electric potential V at a point in an electric field can be defined as the work done EW in bringing unit
Q
positive charge Q from infinity to that point in the electric field. This gives us V = 4πℇ ∂r and V =
W
where
Q
the
unit is J/C
Motion in an Electric Field
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Millikan’s experiment concludes that any charge must be a multiple of the electronic charge, 1.6 x 10 -19 C. Thus, we say
that charge is 'quantised', that is it comes in quanta or lumps all the same size.
The electronvolt is equal to the kinetic energy gained by an electron when it is accelerated by a potential difference of
-19
one volt. 1eV = 1.6x10
J.
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The equation for a charged particle moving through voltage V is V = √
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2QV
m
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derived from mv 2 = QV
2
Magnetic Fields
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An atom consists of a nucleus surrounded by moving electrons. Since the
electrons are charged and moving, they create a magnetic field in the space
around them.
Iron, nickel and cobalt belong to a class of materials that are ferromagnetic. In
these materials, the magnetic fields of atoms line up in regions called magnetic
domains. If the magnetic domains in a piece of ferromagnetic material are
arranged so that most of their magnetic fields point the same way, then the
material is said to be a magnet and it will have a detectable magnetic field.
The strength of a magnetic field at a point is called the magnetic induction and
is denoted by the letter B. It is measure in (T)
For a straight conductor of length l in a uniform field B, the force on the conductor becomes
F = BILsinθ
If the conductor is parallel to the field, sinθ = 0 and the force is zero.
The force is maximum when the current is perpendicular to the magnetic induction.
If a charge’s velocity vector is not perpendicular to the magnetic field, then the component
of v perpendicular to the field v⊥ must be used in the equation F = BILsinθ.
To find Magnetic induction at a distance from a long current carrying wire
μσI
B = 2πr
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Comparison of forces (gravity is weaker than electric)
The speed of light can be found using the permeability of free
1
space and the permittivity of free space c =
√(ε0 μ0 )
Capacitors
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Capacitors store charge and energy
The capacitance of a capacitor is a measure of how much
charge it can store per volt across it.
Capacitance is measured in farads (1 F = 1 C V-1 )
The time taken for a capacitor to charge depends on the size of the capacitor (C) and the resistance of the
charging circuit (R)
Bigger values of C & R result in longer charging and discharging
times.
The product of resistance and capacitance is called the time
constant of the circuit.
The time constant gives the time taken for a capacitor to charge to
63%
𝜏 = 𝑅𝐶
A capacitor is said to be fully charged (or discharged) after 5-time constants.
Capacitor’s block d.c. When a capacitor is full, no more current flows.
Capacitors will allow an alternating current (AC) to flow. This is because the capacitor lets charge move onto it
as it charges, and off it as it discharges. So, charge can move in an alternating
fashion.
The effective rate of flow of charge (Irms) onto and off a capacitor depends on
the size of the capacitor and the frequency of the a.c. supply.
The bigger the capacitor and higher the frequency, the easier it is for charge to
continually move in the circuit.
A capacitor’s opposition to a.c. is called capacitive reactance (Xc)
1
Xc =
Reactance is similar to resistance in d.c. circuits but is frequency
2πfc
dependent.
Reactance is measured in ohms. (Ω) X c =
V rms
I rms
Inductors
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An inductor is a component that has similar properties to a capacitor in that it can store energy and “reacts”
to different frequencies in an a.c. circuit.
A capacitor stores energy in an electric field; an inductor stores energy in a magnetic field.
An inductor is basically a coil of wire with negligible resistance that uses the growth and decay of a magnetic
field in its operation.
If a magnet is moved in and out of a coil of wire, an alternating voltage is induced in the
coil.
The size of this induced voltage depends on the size/ core of the coil, the strength of the magnet and the rate
of change of the motion of the magnet
This induced voltage does not require any external power supply and is therefore called the self-inductance of
the coil.
In a d.c. circuit, when the circuit is turned on, the sudden change in current produces
a changing magnetic field around the coil that induces an Emf across the coil that
opposes the change in current that causes it.
The induced Emf in a coil always opposes the change that causes it. (This is called
Lenz’s Law)
This induced Emf is called a “Back-Emf” (because it opposes the forward supply
voltage)
When the circuit is initially switched on, there is a large “rate of change” of current. (This is the gradient of the
current time graph)
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This causes a large changing magnetic field around the inductor which in turn induces a large back-emf across
the coil.
This back-emf “slows” the rate of change of current which causes the back-emf to decrease.
The graph shows the gradient (dI/dt) decreasing to zero as the back-emf decreases to zero as the current
reaches its maximum value
At the instant of “switch-on” the back-emf is equal and opposite to the supply voltage
The growth and decay graphs of current in an inductor in a d.c. circuit are similar to the
charge and discharge graphs of voltage for a capacitor.
When switched on, it takes time for the current to reach its maximum value. Similarly,
when switched off, it takes time for the current to fall to zero
The inductance of an inductor is the ratio of the induced back-emf to the rate of
change of current.
dI
ε = −L ( ) where L is the inductance measure in (H),  is the back
dt
EMF in (V) and dl/dt is the rate of change of current
Inductors store energy in the magnetic field around them. This energy
can be released when the field collapses and a large emf is produced.
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The energy stored in an inductor is given by: E = LI 2
2
This energy can be released very quickly when a large coil is switched
off. This can cause a large spark which can damage equipment, loss of data or cause an electric shock.
An inductor is another frequency dependent component.
When placed in an a.c. circuit the inductor has an inductive reactance (XL) that depends on the inductance of
the inductor, L, (in henrys) and the frequency, f, of the a.c. supply
X L = 2πfL Reactance is similar to resistance in d.c. circuits but is frequency dependent.
Reactance is measured in ohms. (Ω)
A defibrillator or AED is used to restart the normal beating of a person’s heart.
Capacitor is charged up to a high voltage.
Switch is pressed and the capacitor is discharged through the patient.
The inductor is used to oppose the change of the current and ensures that the current is delivered to the
patient at a high enough level for the required time
A inductor is used (instead of a resistor) to ensure all the energy is passed to the patient and not wasted as
heat in a resistor.