  I investigate the effect of non-uniform magnetic fields in the extended
structures of radio galaxies on the observed synchrotron and inverse-Compton
emission. On the assumption of an isotropic field, with a given power spectrum
and a Gaussian distribution of the Cartesian components of the magnetic field
strength, I derive a simple integral that can be used numerically to calculate
the synchrotron emissivity from any electron population. In the case of
power-law spectra, I show that it is possible to estimate the difference
between the synchrotron emissivity from a region with such a field and that
from the commonly assumed arrangement where $B$ is constant everywhere, though
fully tangled, and that this difference is small, though it increases if the
electron energy density scales with the field. An aged electron spectrum in
such a field produces a characteristic curved synchrotron spectrum which
differs significantly from the classical Jaffe-Perola spectrum, and I discuss
some effects that this might have on standard spectral age fitting. Finally, I
show that inverse-Compton scattering of the cosmic microwave background is only
moderately affected by such a field structure, with the effects becoming more
important if the electrons follow the field. Magnetic-field estimates in the
literature from combined synchrotron and inverse-Compton modelling will give
reasonable estimates of the mean magnetic field energy density if the field is
non-uniform but isotropic.
