Electricity and magnetism Core / HL
5 - SL
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Electric field: area around a charge where a small test charge will experience a force
Electric field strength: force per unit charge experienced by a small test charge when placed in
an electric field E = Fq
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Coulomb's law: any two charge will experience a force which is proportional to the product of
their
charges and inversely proportional to the distance between them squared →
qQ
r2 where
2 −1 −2
C N m )
F =k
8.85×10^(−12)
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k=
1
4πε0
(​ε​0 is called the electric permittivity of vacuum and ​is
Relationship between electric field strength and Coulomb’s law: E =
F
q
and F = k
qQ
r2
, so
and
ELECTRIC CURRENT:
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Electric current is the flow of electrons (in conductors) or ions (in solutions)
Δq
Current (I) is the rate of flow of charge and is measured in Ampere (A) → Δt
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In a conductor, I = nAvq
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The potential difference ​V ​between two points is the work done per unit charge to move a
point charge from one point to the other. V is measured in Volt (V) and V = Wq
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Whenever there is a potential difference there has to be an electric field.
We define the electron volt as the work done when a charge equal to one electron charge is
taken across a potential difference of one volt → 1eV=1​.6​ ×10​−19 ​C×1V=1​.​6×10​−19 ​J
RESISTANCE AND ITS RELATIONSHIP WITH I AND V:
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The electric resistance ​R ​of a conductor is defined as the potential difference ​V ​across its ends
divided by the current ​I ​passing through it. R = VI
Ohm’s Law → ​I​∝​V
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It is found from experiment that the electric resistance ​R ​of a wire (at fixed temperature) is
proportional to its length ​L a​ nd inversely proportional to the cross-sectional area ​A: R = ρ AL
The constant ​ρ i​ s called resistivity and depends on the material of the conductor and the
temperature
Electric Power: work done per unit time. P = V I = I 2 R =
V2
R
CIRCUITS:
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IN SERIES:
R= R1 + R2 + R3
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I= I 1 = I 2 = I 3
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V= V 1 + V 2 + V 3
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​IN PARALLEL:
1
1
1
1
R = R + R + R
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I= I 1 + I 2 + I 3
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V= V 1 = V 2 = V 3
1
2
3
EMF:
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Electromotive force: the emf of a cell is the work done per unit charge in taking the charge
from low (-) to high (+) potential
emf= I (R + r)
MAGNETIC FIELDS:
● Grip rule: Grip the wire with the fingers of the right hand in such a way that the
thumb points in the direction of the current. Then the direction in which the fingers
curl is the direction of the magnetic field vectors.
● There is no magnetic force on a moving charge if the charge moves along the field
direction.
● If the magnetic force is ​F when a charge q moves with speed v making an angle ​θ ​with the
direction of the field, then the magnitude of the field, B, also called the magnetic flux density,
is
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A charge q moving with speed v in a region of magnetic eld of magnetic ux density B will
experience a magnetic force F given by → F=qvBsin​θ
The formula for the magnetic force on a length L (L is that length of the wire that nds itself in
the region of the field) is: F=BILsinθ
To find the direction of the force, use the right-hand rules