New types of cone solutions for liquid-liquid (or gas-liquid) interfaces subjected to electric fields are described as a function of the permittivity ratio in the limit of perfectly insulated liquids. The relevance of these solutions is discussed in relation to recent numerical findings by several authors. A discussion is also made of approximate conical solutions for de fields as a function of the conductivity ratio for liquid-liquid systems. The classical Taylor cone solution corresponds to the case of infinite conductivity of the inner liquid.