43. We assume there is charge qon one plate and charge –qon the other. The electric field in the lower half of the region between the plates is EqA110=κε,where Ais the plate area. The electric field in the upper half is EqA220=.Let d/2 be the thickness of each dielectric. Since the field is uniform in each region, the potential difference between the plates is VEd EdqdAqdA=+=+LNMOQP=+120120222112εκκεκκ, so CqVAd==+22.This expression is exactly the same as that for Ceqof two capacitors in series, one with dielectric constant 1and the other with dielectric constant 2. Each has plate area
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