2.2 motion of charged particles in electric fields

draw and describe the electric field produced by two oppositely charged parallel conducting plates

• uniform between the plates and away from the edges is uniform

• represented by evenly spaced electric field lines

• means a positive test charge experiences the same force no matter where it is placed

• near and beyond the edges of the plates the electric field is non-uniform

derive the formula for the accelleration of a charge q of mass m in an electric field

how do cyclotrons utilise electric fields

• cyclotron is composed of two hollow D-shaped copper conductors called Dees

• the potential difference in the gap between the dees produces a uniform electric field

• when the charges enter the electric field they are accellerated as the electric field exerts a force on the charges, due to f=ma, the charges gain speed

• the magnetic field created by electromagnets above and below the dees cause the charged particles to move in a semi circular path through the dees so that they return to the electric field

• the electric field is reversed when the charges return to the gap so that they once again accellerate accross the electric field

• the process repeats many times and the charges eventually exit the cyclotron having accumulated a large amount of kinetic energy and thus speed

• the charges do not gain energy while inside the dees as there is no electric field within a hollow conductor

describe the morion of charged particles at an angle to a uniform electric field

• consider a negative charge entering a uniform electric charge between two parallel conducting plates

• the charge enters in a direction which is perpendicular to the electric field

• the electric field exerts a constant force towards the lower plate

• the electric field does not exert a force on the charge in the horizontal direction

• therefore the component of velocity perpendicular to the electric field remains constant

• results in a parabolic path towards lower plate

• the magnitude of vertical accelleration of a charge can be calculated using a=(qE)/m

• the direction depends on the particle’s charge and the charge of the plates of the conductors