Particles can be deflected using both electric fields and magnetic fields. Deflecting beams of charged particles is required in multiple applications from television sets to circular accelerators.
A beam of electrons, like that from an electron gun, can be deflected if they pass through an electric field.
From the revision topic on electric fields the strength of the uniform electric field between the two plates above is given by:
The vertical (in this case downwards) force acting on the particles is given by:
Combing the two equations gives the vertical force on a particle being deflected through a uniform electric field as:
This equation and be combined with newtons second law () to create an equation for the vertical acceleration of the particle in the beam:
The stronger the field the more the particle will be deflected.
A beam of electrons are deflected by an electric field made from two parallel plates 2.5cm apart with a potential difference of 1000V. Calculate (a) the strength of the electric field (b) the vertical force acting on the electrons in the beam and (c) the acceleration of the particles in the beam
(a) the strength of the electric field is calculated like so:
(b) the vertical force is given by where q, in this example is the charge on the electron (
)
(c) acceleration is given by where m, the mass of an electron, is
:
This acceleration may seem very large however the value is given in seconds but the particles are only accelerated for nanoseconds.
Magnetic fields exert a force on a moving charge of magnitude:
Where:
is the charge
is the speed of the charge
is the magnetic field strength
As this force acts perpendicular to the a particle's motion it is centripetal and causes the particle to curve in an arc of a circle. The equation for centripetal force is:
In a uniform field this equation can be combined with the force on a charge in a magnetic field equation above:
This equation can then be rearranged to allow the radius of the arc and speed of the particle to both be easily calculated.
An electron travelling at 10% the speed of light is deflected using a magnetic field with a strength of 0.1Tesla. Calculate (a) the force on the electron and (b) the radius of the arc the electron follows
(a) Firstly the speed of the electron must be calculated:
Then the force can be calculated:
(b) To calculate the radius the equation is used:
Multiply by
divide by
Cancel out one of the
The radius can now be calculated:
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