A regular icosahedron, as shown in the figure, has an outerradius (defined as the distance from the centre to a vertex) of9.51 cm and an inner radius (defined as the distance from thecentre to the centre of a face) of 7.56 cm. It has 20 faces whichare equilateral triangles with side length 10.0 cm, and 12vertices.
Twelve negative charges of magnitude 20.0 μC are placed at thevertices and 20 positive charges of magnitude 12.0 μC are placed atthe face centres. A positive charge of Q = +44.25 μC is placed atthe centre of the icosahedron.
What is the force acting on the charge at the centre of theicosahedron? [1]
If one of the negative charges at a vertex is removed, what isthe force on the charge at the centre of the icosahedron? [2]
If one of the positive charges at the face is removed, what isthe force on the charge at the centre of the icosahedron? [2]
Using your answers to parts ii) and iii) what is the net forceon the charge Q at the centre if a complete face (i.e. one positivecharge and the three surrounding negative charges), is removed?[5]
