Developing device, process cartridge, and image forming apparatus

A developing device configured to develop a latent image, comprising:

• a latent image carrier configured to carry a latent image;
• a toner carrier configured to carry toner and develop the latent image, said toner carrier being arranged opposing the latent image carrier;
• at least two electrodes configured to create an electric field therebetween, said at least two electrodes being arranged in a prescribed direction insulated from each other on a surface of the toner carrier;
• and
• an alternating voltage supplying device configured to supply n number of phases (n ≧2) of an alternating voltage to the at least two electrodes, respectively, said alternating voltage changing the electric field to cause toner to hop and form toner cloud on the surface of the toner carrier;
• wherein
• said toner hopping is halted at a prescribed time period during the toner cloud formation,
• said alternating voltage is supplied a prescribed times “m” in a cycle T1 per cycle T2, T2>Ti×m,
• r represents a width of a developing nip where the latent image carrier and the toner carrier oppose each other to develop the latent image in a moving direction of the latent image carrier, h represents a parameter, and Vp represents a line speed of the latent image carrier, and
• r/Vp =h×1/n×T2/m
• (1<h <400).