16 CHARGE AND FIELDAccelerating charges

• Derive relativistic expressions for momentum and energy

• Solve problems involving particles accelerated to close to the speed of light

Electric fields

• Define the term electric field

• Investigate uniform electric fields and plot equipotentials

Uniform fields and Millikan’s experiment

• Derive the relation E = -V/d for a uniform

electric field

• Explain the principles of Millikan’s experiment for determining the charge on an electron

Deflection by electric fields

• Observe, model and explain the deflection of an electron beam in a uniform electric field

Deflections of electron beam by electric field

electron gun deflection plates

zero potential

hotcathode

spacing d

_

anode+ +V

acceleratingpotential difference

vertical force F = eE = e Vd

_

horizontalacceleration

_

constant velocity

_

vertical accelerationconstant horizontal velocity resultant velocity

_

force

F = e Vd

electric field E = Vd

Deflection by magnetic fields

• Explain why charged particle beams follow circular paths when injected perpendicular to a magnetic field

• Determine e/m from experimental data

The bubble chamber track shown above represents a charged particle entering from the left. 1. The magnetic field is directed into the screen. Is the charge on

the particle + or -?2. Sketch the track for another particle of opposite charge to the

first entering from the right.3. Sketch the track of a particle entering from the left, with the

same charge as the first one, but greater kinetic energy.

Particle accelerators

• Explain principles of circular accelerators

• Explain the need for large radius accelerators (synchrotron effect)

What is the main drawback of a linear particle accelerator? (p168)

What is main the advantage of a circular accelerator over a linear one?

For really high energy particle beams in a circular accelerator, why does the ring need to have a very large radius?

How can scientists take advantage of the energy radiated when charged particles are centripetally accelerated? (Hint: the answer is nearby)

Crossed electric and magnetic fields

• Explain the principle of, and model, an ion velocity selector that uses perpendicular electric and magnetic fields

Non uniform fields

• Learn how to characterise field strength in terms of density of field lines

• Use symmetry and geometry arguments to determine field strengths

Field-potential relations and Coulomb’s Law

• By analogy with the gravitational case, deduce the relationship between electric field and potential

• Learn and apply Coulomb’s Law