  We present a thorough analysis of the electronic detection of charged
particles, confined in a Penning trap, via image charges induced in the trap
electrodes. Trapping of charged particles in an electrode structure leads to
frequency shifts, which are due to image charge and space charge effects. These
effects are of importance for Penning trap experiments which involve high
charge densities or require high precision in the motional frequencies. Our
analysis of image charges shows that only (higher order) odd powers of the
particle displacement lead to induced charge differences, giving rise to a
signal. This implies that, besides the centre-of-mass frequency of a trapped
particle cloud, also higher order individual particle frequencies induce a
signal, which can be picked up by an electronic detection circuit attached to
the trap electrodes. We also derive analytic expressions for the image charge
and space charge induced frequency shifts and perform simulations of space
charge effects. In relation to this, we discuss the consequences of the shifted
particle frequencies for resistive cooling of the particle motion.
