Abstract: A magnetically shielded conductor assembly containing a conductor disposed within an insulating matrix, and nanomagentic material and nanoelectrical material disposed around the conductor. The conductor has a resistivity at 20 degrees Centigrade of from about 1 to about 100 microohm-centimeters. The insulating matrix is composed of nano-sized particles having a maximum dimension of from about 10 to about 100 nanometers. The insulating matrix has a resistivity of from about 1,000,000,000 to about 10,000,000,000,000 ohm-centimeter. The nanomagnetic material has an average particle size of less than about 100 nanometers. The nanomagnetic material has a saturation magnetization of from about 200 to about 26,000 Gauss. The magnetically shielded conductor assembly is flexible, having a bend radius of less than 2 centimeters.