Skip over navigation
Hold Still Please
Age 16 to 18
Challenge Level 
Why do this problem?
This problem will develop students' intuition and skill with vectors and force laws in a context which encourages exploration and does not require any calculation to get started. By trying to construct stable configurations students will be led towards the notion of static points only occurring at places of zero electrostatic potential.Possible approach
This problem is very open and well suited to discussion to get
things started. The main requirement is the encouragement that
students start to try out specific configurations and then use the
force law to determine whether or not the configuration will remain
static.
More general statements are, of course, more subtle and
difficult to analyse than particular examples. Clear, systematic
thinking will be needed, as will a clear
representation system (diagrammatically or
algebraically).
After doing this problem, you might refer students to
'Earnshaw's theorem' http://en.wikipedia.org/wiki/Earnshaw%27s_theorem
Key questions
Are there any obvious simple cases to look at?
Can you make any symmetrical configurations to look at?
What is special, if anything, about configurations in which
$1$ or more particles don't move?
How might you attempt to fix down a configuration which will
move by adding more fixed particles?
Possible extension
Take an entirely stable configuration. Consider the question:
what happens if you nudge one of the particles slightly?
Possible support
Concentrate on intuitive attempts at the problem.
You may also like
Lunar Leaper
Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?
Whoosh
A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?