The electric field outside the balloon at all points in space is ω/ε where ω = Q/4πa^2.
To find the electric field(E) due to a symmetrical surface, Gauss’ Law is used, which is
E x (ds) = q/ε
Here ds = surface area of the surface
And Q = charge enclosed by the surface
As the balloon is spherical with radius a, its area will be 4πa^2
Putting the values in the above equation
E x 4πa^2 = Q/(ε)
E = Q/4πa^2(ε)
The surface charge density(ω) = Q/4πa^2
Hence
E = ω/ε
Thus, The electric field outside the balloon at all points in space is ω/ε where ω = Q/4πa^2.
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