The shield strongly attenuates the electric field noise. Core to shield capacitance is added to the stray capacitance, increasing ground currents in the loop. These currents generate a magnetic field. It is important to minimize the area of this loop as far as possible by routing the cable close to grounded metalwork.
Occasionally, a technician or service person will ask me, "why not just increase the output by increasing the voltage (the current flow) to the motor?" While that may seem logical, increasing the voltage (in effect, creating an overvoltage situation) will not necessarily boost the output of the device. To understand why, you need to become familiar with a physical characteristic called "hysteresis loss."
There are two ways to overcome this problem. One is to use a kind of electric current that periodically reverses direction, which is known as an alternating current (AC). In the kind of small, battery-powered motors we use around the home, a better solution is to add a component called a commutator to the ends of the coil. (Do not worry about the meaningless technical name: this slightly old-fashioned word "commutation" is a bit like the word "commute". It simply means to change back and forth in the same way that commute means to travel back and forth.) In its simplest form, the commutator is a metal ring divided into two separate halves and its job is to reverse the electric current in the coil each time the coil rotates through half a turn. One end of the coil is attached to each half of the commutator. The electric current from the battery connects to the motor electric terminals. These feed electric power into the commutator through a pair of loose connectors called brushes, made either from pieces of graphite (soft carbon similar to pencil "lead") or thin lengths of springy metal, which (as the name suggests) "brush" against the commutator. With the commutator in place, when electricity flows through the circuit, the coil will rotate continually in the same direction.
Think of the atoms of magnetic material as an unruly herd of cattle. Running electric current through the material will polarize these atoms, creating the magnetic field. But as I mentioned, this is an unruly herd, so it takes time for the current to bring all those atoms into formation.