Question about the length of antenna
The 1/4 wave monopole antenna relies on the earth or a counterpoise to form the other half of the antenna.

In general, nearly any conducting material can act as an antenna. The issue to to design an effective antenna for the application. In antenna engineering, the primary design factors are directivity, efficiency, radiation resistance, and pattern. Secondary considerations are feedpoint impedance, cost, size, feasibility, and maintainability.

A loop antenna that has a perimeter &lt; 0.1 wavelengths long (Cλ) can be treated as an antenna with uniform current. As a result, the maximum directivity of a small loop antenna can be shown to be 1.5. This directivity is multiplied by efficiency to determine the gain of the antenna. A 100% efficient antenna of this type would therefore have a 1.5 dBi gain. The efficiency is primarily determined by the RF resistance of the conductor (due to skin depth and connection losses) and ground losses due to proximity to the ground (depending upon the orientation of the antenna). 

The radiation resistance in ohms of a small loop can be computed as 197*Cλ4n2 where N is the number of turns.

A small loop antenna will have a radiation pattern similar to the shape of a doughnut. The primary gain direction is off the edges of the plane containing the loop.