A regular icosahedron, as shown in the figure, has an outer radius (defined as the distance...

A regular icosahedron, as shown in the figure, has an outer radius (defined as the distance from the centre to a vertex) of 9.51 cm and an inner radius (defined as the distance from the centre to the centre of a face) of 7.56 cm. It has 20 faces which are equilateral triangles with side length 10.0 cm, and 12 vertices.
Twelve negative charges of magnitude 20.0 μC are placed at the vertices and 20 positive charges of magnitude 12.0 μC are placed at the face centres. A positive charge of Q = +44.25 μC is placed at the centre of the icosahedron.

What is the force acting on the charge at the centre of the icosahedron? [1]
If one of the negative charges at a vertex is removed, what is the force on the charge at the centre of the icosahedron? [2]
If one of the positive charges at the face is removed, what is the force on the charge at the centre of the icosahedron? [2]
Using your answers to parts ii) and iii) what is the net force on the charge Q at the centre if a complete face (i.e. one positive charge and the three surrounding negative charges), is removed? [5]

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Expert Solution

genius_generous answered 1 year ago

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