Does a metal back box need to be earthed?
Correspondingly, does a metal box have to be grounded?
The only requirement is that the application is grounded. Metal-sheathed wiring depends on bonding with the metal electrical box for grounding. Using metal-sheathed wiring with plastic electrical boxes, without taking other grounding measures, severs that ground and is highly dangerous.
Also, do sockets need to be earthed?
Fixed wiring devices – including socket outlets – should not be wired with flex. An earth conductor insulated with green and yellow sleeving should be fitted between the earth terminal of the socket and the earth terminal of metal back boxes so that the metal box is earthed.
The appliance will operate normally without the ground wire because it is not a part of the conducting path which supplies electricity to the appliance. In the absence of the ground wire, shock hazard conditions will often not cause the breaker to trip unless the circuit has a ground fault interrupter in it.