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An insulated metal sphere of radius 
is situated in a vacuum. The charge 
on the sphere may be considered to be a point charge at the centre of the sphere. Define capacitance and hence show that the capacitance 
of the sphere is given by the expression
An isolated metal sphere has radius 
.
Use the expression in (a)(ii) to calculate the capacitance, in picofarad, of the sphere.
The sphere is charged to a potential of 
. A spark occurs, partially discharging the sphere so that its potential is reduced to 
. Determine the energy of the spark.
.
