What are the mathematical purposes of doing earthing of the electrical applieces ?

Not sure what you mean by "mathematical purposes" in your question. Earthing ( or "grounding" as we say in the US) is typically done for (a) safety reasons - to prevent the possibility of an internal short between the chassis and power supply from energizing the chassis, or (b) to prevent electromagnetic interference between the applicance and other devices - so that the appliciance doesn't emit excessive electromagnetic radiation (which could adversely affect the performance of other appliances) and also so that the applicance isn't adversely affected by external EMI from other sources. For EMI protection the appliance has a metal or otherwise conductive case which is earthed (a good example is your PC).

Another reason is to make sure all exposed metal surfaces are at the same potential.

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Originally Posted by zaharely

what are the mathematical purposes of doing earthing of the electrical applieces ?

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Earthing is important to ensure that all electrical appliances carry the same surface voltage (nil in respect to earth). Electrical equipment may leak by accident, or pulse suppression equipment may cause surfaces to carry unwanted voltages. To prevent that, earthing is therefore required, and essential for safety.

Earting is basically meant for human safety first. Then equipment. In india earthing is done in accordance with is:3043 & internationally ieee-80. The purpose is not to shoot up panel / equipment body potential than the ground potential. Thus, the person, standing on ground, even if anybody; advertantely / inadvernantly comes in contact with panel body / equipment, should not get electrical shock. Also, at the same time, if leaked voltage is at such a high level; and of the range to operate protective relays, the circuit breaker will trip off / fuses will blow.