Which type of electrical equipment does not require a magnetic field for its operation?

The correct answer is the electrostatic voltmeter, as this type of electrical equipment operates based on electrostatic principles rather than relying on a magnetic field. An electrostatic voltmeter measures voltage by detecting the electric field created by a charged conductor. It utilizes a non-contact method to sense voltage levels, allowing for accurate measurements without the need for a magnetic field, which distinguishes it from the other options listed.

In contrast, inductive sensors, relays, and transformers all operate based on the principles of electromagnetism, which fundamentally require the presence of a magnetic field. Inductive sensors detect changes in magnetic fields, relays use electromagnetic fields to open or close circuits, and transformers rely on magnetic fields for transferring electrical energy between circuits through electromagnetic induction. Thus, the electrostatic voltmeter stands out as an instrument that functions independently of magnetic influences.