Context :

Aims : We study the intra-cluster magnetic field in the poor galaxy cluster Abell 194 by complementing radio data , at different frequencies , with data in the optical and X-ray bands .

Methods : We analyze new total intensity and polarization observations of Abell 194 obtained with the Sardinia Radio Telescope ( SRT ) .
We use the SRT data in combination with archival Very Large Array observations to derive both the spectral aging and Rotation Measure ( RM ) images of the radio galaxies 3C 40A and 3C 40B embedded in Abell 194 .
To obtain new additional insights in the cluster structure we investigate the redshifts of 1893 galaxies , resulting in a sample of 143 fiducial cluster members .
We analyze the available ROSAT and Chandra observations to measure the electron density profile of the galaxy cluster .

Results : The optical analysis indicates that Abell 194 does not show a major and recent cluster merger , but rather agrees with a scenario of accretion of small groups , mainly along the NE-SW direction .
Under the minimum energy assumption , the lifetimes of synchrotron electrons in 3C40 B measured from the spectral break are found to be 157 \pm 11 Myrs .
The break frequency image and the electron density profile inferred from the X-ray emission are used in combination with the RM data to constrain the intra-cluster magnetic field power spectrum .
By assuming a Kolmogorov power law power spectrum with a minimum scale of fluctuations of \mathrm { \Lambda _ { min } = 1 kpc } , we find that the RM data in Abell 194 are well described by a magnetic field with a maximum scale of fluctuations of \mathrm { \Lambda _ { max } = ( 64 \pm 24 ) kpc } .
We find a central magnetic field strength of \mathrm { \langle B _ { 0 } \rangle = ( 1.5 \pm 0.2 ) \mu G } , the lowest ever measured so far in galaxy clusters based on Faraday rotation analysis .
Further out , the field decreases with the radius following the gas density to the power of \eta =1.1 \pm 0.2 .
Comparing Abell 194 with a small sample of galaxy clusters , there is a hint of a trend between central electron densities and magnetic field strengths .

Conclusions :