# Electrical work

Electrical work refers to the work which is done on an electrically charged particle by an electric field. This form of energy is expressed on similar lines to the mechanical work that is done by a force. The basic equation for work done due to an electric field is:

W = q ∫E.dr

where q stands for the charge of the particle, E stands for the strength of the electric field and r is the distance involved in the exertion of the electric field. The electric field is essentially the force per unit charge, and hence by multiplying the charge by the separation between positive and negative regions of field, the work per unit charge is obtained.

It requires positive external work to move a positive charge into a region possessing a higher value of voltage. This is because external work is needed to be done against the field of the electric force. Similarly, it requires positive external work to transfer a negatively charged particle from a region of higher voltage to a region of lower voltage.

Under normal circumstances, positively charged particles that are free to move will always tend to shift towards the direction of lower voltages. In contrast to this behavior of positive charges, particles that are negatively charged tend to shift towards regions that possess lower voltage.

The electric work which is done by an electric field is independent of the path followed by the carriers of charge. There is no change in the voltage around any closed path; this fact is brought out by the observation that when returning to the starting point in a closed path, the net of the external work done is zero. The same phenomenon holds good for electric fields as well.

The fact explained above forms the basis of one of the most fundamental laws governing electrical and electronic circuits, the Kirchoff's voltage law. According to this principle, the voltage gains and the drops that occur around any electrical circuit loop is always equal to zero.