  We obtain the electromagnetic form factors of the $\gamma N\Delta$ transition
by analyzing recent pion-electroproduction data using a fully relativistic
dynamical model. Special care is taken to satisfy Ward-Takahashi identities for
the Born term in the presence of form factors thereby allowing the use of
realistic electromagnetic form factors of the nucleon and pion. We parametrize
the $Q^2$ dependence of the {\it bare} $\gamma N \Delta$ form factors by a
three-parameter form which is consistent with the asymptotic behavior inferred
from QCD. The parameters of the bare $\gamma N \Delta$ form factors are the
only free parameters of the model and are fitted to the differential
cross-section and multipole-analysis data up to $Q^2=4$ (GeV/c)$^2$ in the
$\Delta(1232)$-resonance region. This analysis emphasizes the significance of
the pion-cloud effects in the extraction of the resonance parameters.
