Bright-rimmed clouds form on the edges of H II regions affected by the high energy radiation from a central ionizing source. The UV radiation from the ionizing source results in compression and ionization causing either cloud disruption or further star formation. In this work, we present R-band polarization measurements towards four bright-rimmed clouds, IC1396A, BRC 37, BRC 38, and BRC 39, located in the different directions of the H II region, Sh2-131, in order to map magnetic fields (B-fields) in the plane of the sky. These BRCs are illuminated by the O star HD206267 and present a range of projected on sky geometries. This provides an opportunity to understand the magnetized evolution of BRCs. The B-field geometries of the clouds deduced from the polarization data, after correction for foreground ISM contamination, are seen to be connected to the ambient B-fields on the large scale. They seem to play an important role in shaping the cloud IC1396A and BRC 37. BRCs 38 and 39 show a broader and snubber head morphology possibly due to the B-fields being aligned with incoming radiation as explained in the simulations. A good general agreement is noted on comparing our observational results with the simulations supporting the importance of B-fields in BRC evolution. This work is the first step towards systematic mapping the B-fields morphology in multiple BRCs in an expanding H II region, extending the work presented by Soam et al. (2017b).
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