Find the maximum directivity of an antenna whose power density is given by $$W_{rad}= \hat{a} \frac{A_{o} \sin \theta}{r^{2}}$$ $$\frac{W}{m^{2}}$$ where $$A_{o}$$ is peak value of power density $$\theta$$ is the usual spherical coordinate and $$hat{ar}$$ is the radial unit vector

A

$$\frac{4}{\pi}$$

B

$$\frac{2}{\pi}$$

C

$$\frac{3}{\pi}$$

D

$$\frac{5}{\pi}$$