A resonant six-turn loop of closely spaced turns is operating at 50 MHz. The radius of the loop is λ/30, and the loop is connected to a 50-ohm transmission line. The radius of the wire is λ/300, its conductivity is σ = 5.7 × 107 S/m, and the spacing between the turns is λ/100. Determine the:

a. the directivity of the antenna (in dB)
b. radiation efficiency taking into account the proximity effects of the turns
c. reflection efficiency gain of the antenna (in dB)