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The plane would be perpendicular to the dipole and passing through it. Do em waves propagate in all directions of that plane or in any direction of any plane?

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    $\begingroup$ All directions. Plus directions that are inclined out of the plane, except for the direction perpendicular to the plane. That is, a dipole radiates in all directions except the direction of the orientation of the dipole. $\endgroup$
    – garyp
    May 14, 2021 at 17:35

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The radiation pattern around an ideal horizontal dipole suspended in 3-D space looks like a vertical torus or doughnut centered on the middle of the dipole. This ideal picture is altered significantly by the presence of the earth's surface when the dipole is less than ~a wavelength from the surface. In this case, the radiation pattern begins to look like two rounded lobes extending at right angles to the direction of the dipole. If closer than that to the earth, the pattern starts looking like one rounded lobe projecting straight up from the antenna, away from the earth.

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