While I was reading 'symmetry' from wikipedia, then I came to this statement:
...For example, an electric field due to a wire is said to exhibit cylindrical symmetry, because the electric field strength at a given distance r from the electrically charged wire of infinite length will have the same magnitude at each point on the surface of a cylinder (whose axis is the wire) with radius r. Rotating the wire about its own axis does not change its position or charge density, hence it will preserve the field. The field strength at a rotated position is the same. Suppose some configuration of charges (may be non-stationary) produce an electric field in some direction, then rotating the configuration of the charges (without disturbing the internal dynamics that produces the particular field) will lead to a net rotation of the direction of the electric field. These two properties are interconnected through the more general property that rotating any system of charges causes a corresponding rotation of the electric field.
Saw the statement? What is the proof afterall behind this statement? Is it applicable to translation of charges also??