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Chapter 16. Charge and Field:
All charged objects have a field around them. Any charged object within this field will be
either attracted or repelled depending on the charges of the 2 objects.
You can work out the force acting upon the objects using Coulomb's Law , F = 2 . F is
the force on each object acting away from the other, so if F is positive, they will be
repelled, if it is negative they will be attracted. Q and q are the charges on the objects and
r is the distance in between them. Finally k is the electric force constant which is given on
the first page of the data booklet for free space. Difference materials will have a different
value of , however, you can calculate k for other values of using the formula given in the
data book, k - .
You should notice similarities between this force and gravity, F= 2 . Both force are
inverse square forces which means, as the objects become closer, the force becomes
stronger at an exponential rate. The difference is the gravitational force is always negative,
so objects are always attracted, however, the electric force can be both positive and
negative, since Q and q can be either, this means electric charges can both attract and
Electric Field Strength (E)
The electric field strength is the force for each unit of charge, Newtons per Coulomb, NC -1.
E= . This is also like gravity, where the gravitational field strength (g) is the force per
unit mass. F=mg, F=qE.
Objects which have their charge at a single point, or can be modelled like that, for example
a charged sphere, have a radial field. Like the gravitational field about a planet. At any
given point the field strength can be worked out as, E = 2 . Which is another inverse
square law. E 2 .
Electrical Potential Energy
The electrical potential energy is the amount of energy required to move an object from
infinity to a distance r from the particle. This means, if the objects are attracted to each
other, then this will be a negative value. Electric Potential Energy can be calculated using
the formula E elec = . So at an infinite distance, Eelec = 0.
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Electrical potential (V) is the amount of electrical potential energy for each unit of charge.
V elec = elec = . Electrical potential (V) is measured in Volts.
A uniform field, is different to a radial field as, the field strength, is constant throughout the
field and can be calculated by E = , where d is the distance between the 2 charges.…read more
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Charged Particles in a Magnetic Field
Current in a wire is the flow of charged electrons, which, like any charged particles, are
effected by a magnetic field. Current (I) is the amount of charge passing through a wire,
per second. I = .
Previously we derived, F = ILB, by combining this with the previous formula, we get,
F= .…read more
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As shown above, a 5MeV particle would, without relativity, go faster than the speed of
light. To take relativity into account we use Einstein's definitions for momentum and kinetic
energy. Firstly momentum, p = m . However, if instead we consider wristwatch time, ,
the time which the object observes, then we get, p = m . Since t = . That
gives us p = m = mv .
For kinetic energy, it's a bit more complicated.…read more