Large-amplitude electromagnetic radiofrequency fields are created by the charge-separation induced in interactions of high-intensity, short-pulse lasers with solid targets and have intensity that decreases with the distance from the target. Alternatively, it was experimentally proved very recently that charged particles emitted by petawatt laser–target interactions can be deposited on a capacitor-collector structure, far away from the target, and lead to the rapid (nanosecond-scale) generation of large quasi-static electric fields ($\mathrm{MV}/\mathrm{m}$), over wide regions. We demonstrate here the generation of both these fields in experiments at the PHELIX laser facility, with approximately $20\;\mathrm{J}$ energy and approximately ${10}^{19}\;\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ intensity, for picoseconds laser pulses, interacting with pre-ionized polymer foams of near critical density. Quasi-static fields, up to tens of kV/m, were here observed at distances larger than $1\;\mathrm{m}$ from the target, with results much higher than the radiofrequency component. This is of primary importance for inertial-confinement fusion and laser–plasma acceleration and also for promising applications in different scenarios.