# How do I express the electric field generated in an antenna as a function of the AC current?

If I have an AC current flowing in a dipole antenna (like the one in the picture), how can I write down a function $$E(t)$$ that depends exclusively on $$I(t)=I_0\sin(\omega t)$$? Note: the function $$E(t)$$ doesn't take in an $$x$$ value because I'm focusing on the electric field at position $$x=0$$.

Also, I've already tried doing $$E(t)=-E_0\cos(\arcsin(\frac{I(t)}{I_0}))$$ , starting from $$E(t)=-E_0\cos(\omega t)$$ and getting $$\omega t$$ from $$I(t)=I_0\sin(\omega t)$$ but when I plot $$E(t)$$ I don't get a cos wave.