How come wires in a cable stay stationary and unaffected by magnetic fields? Every current-carrying wire creates a magnetic field around it. Other wires in that magnetic field feel a force given by F=I(lxB) where B=$\frac{µ0 x I}{2π x R}$. How come wires that are very close to each other, for example in charging wires that have significant current, stay stationary and don't move?
 A: They are not stationary.  
It takes quite a bit of current to see motion (that would also depend on the mass of the wires).
The effect of this physical motion is eventually noticeable in wires wrapped closely together in a solenoid: over time, the insulating cladding between the wires wears out through friction and results in short circuits and quite spectacular "explosions".  
This was a significant problems in labs where intense but spatially homogenous magnetic fields were needed: the solenoid was the best way to  produced intense fields but could "wear out" quite quickly.
A: They are affected. You cannot see the effect because the force is small compared with other forces keeping the wires in place - eg friction.
eg If the current in each wire is $1A$ and the separation is $1cm$ then the force is $2\times 10^{-5}Nm^{-1}$ whereas the weight of $1m$ of such wire is about $0.1N$, so the friction force will probably be in the range $0.01-0.1N$. 
In one common elementary teaching demonstration the "wires" are long, light strips of aluminium foil suspended loosely between supports. It takes very little force to make them move, as you can verify by blowing on them. 
Reference : HyperPhysics online calculator for force between parallel currents.
A: When an electric arc furnace is 'struck' to begin the arcing/steel melting process, you can actually see the high-amperage insulated conductors bend towards each other.
This high current creates an incredible flux around each conductor, thick cables saddled about 1m apart to the concrete wall.
