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In this paper, simple explicit formulas are derived for six components of the electromagnetic field in air from a horizontal electric dipole over a planar perfect conductor coated with a uniaxially anisotropic layer. The total field consists of the direct field, the ideal reflected field or field of an ideal image, the lateral-wave field, and the trapped-surface-wave field. The computations and discussions show that the trapped surface waves including the electric-type and magnetic-type trapped surface waves cannot be neglected when the dipole and the observer are on or close to the surface of the uniaxially anisotropic layer. Both trapped surface waves of electric type and magnetic type attenuate exponentially in the zˆ direction. The wave numbers in the ρˆ direction of electric-type trapped surface wave, which are between k0 and kL, are different from those of the magnetic-type trapped surface wave, which are between k0 and kT. The electric-type trapped surface wave can be excited efficiently when the thickness l of the uniaxially anisotropic layer satisfies the condition 0<(kT/kL) (kL2-k02)12/·l<π and the magnetic-type trapped surface wave can be excited when the thickness l of the dielectric layer satisfies the condition (π/2)<(kT2-k02)12/·l<π. When the thickness l of the uniaxially anisotropic layer satisfies nπ<(kT/kL) (kL2-k02)12/·l<(n+1)π, there are n+1 modes of the electric-type trapped surface waves to propagate along the uniaxial surface, and when the thickness l of the uniaxially anisotropic layer satisfies (n-(1/2))π<(kT2-k02)12/·l<(n+(1/2))π, there are n modes of magnetic-type trapped waves to propagate along the uniaxial surface. When the conditions k0ρ≫1 and z+d≪ρ are satisfied, both the electric-type and magnetic-type lateral waves with the wave numbers being k0 are excited.