A simple derivation is given for the leading term (n = 1) in the Schwinger formula for the pair creation by a constant electric field. The same approach is applied then to the charged-particle production by a charged black hole. In this case, as distinct from that of a constant electric field, the probability of the charged-particle production depends essentially on the particle energy. The production rate by black holes is found in the nonrelativistic and ultrarelativistic limits. The range of values for the mass and charge of a black hole is indicated where the discussed mechanism of radiation is dominating over the Hawking one.