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 $x=0$.

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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.


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