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Electric Potential and Charged Particle Acceleration
If a charge is moved in an electric field, then work is done/energy is converted.
The potential V at a point in a field is the work done W per unit charge q in taking positive charge
from infinity to that point.
V = W
Around a spherical conductor, carrying charge Q:
V = kQ
Where r is the distance of the point from the centre of the charge Q.
V is a scalar quantity
The electric field strength is equal in magnitude to the potential gradient
Positive charges move down a potential gradient ( from high to low potential)
Negative charges move up a potential gradient (from high to low potential)
The relationship between V and distance is inversely proportional
Points that are at the same potential lie on equipotential surfaces. Around a spherical charge, these
are concentric spheres or circles in two dimensions. Equipotential surfaces are always perpendicular
to field lines.
Motion of charges particles
The idea of potential can be used to describe the acceleration of charged particles. It follows from
the definition of the volt that the kinetic energy gained by a particle carrying a charge q when
accelerated through a potential difference of V volts is given by:
1 mv² = QV
Where m is the mass of the particle and v is its subsequent speed.
This equation can be used to calculate the speed of an electron as it emerges from an electron gunm
as used in televisions. The deflection of these electrons across the screen is also caused by electric
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Charged particles are deflected by electric fields and it follows from the definition of electric field
strength that the force F on a particle carrying a charge Q in a field of strength is given by:
F = EQ
If the field is provided by a pair of parallel plates the shape of the path is as shown below and the
F = VdQ
The force is always parallel to the field lines
The path of the particles is a…read more