We consider the excitation of terahertz (THz) electromagnetic fields by interaction of radially polarized laser pulses of diverse profiles with a homogenous plasma density slab. We utilize the properties of the laser pulse to generate THz fields in a plasma slab. It is shown that the radial ponderomotive force exerted by laser imparts an oscillatory velocity to plasma electrons and drives a nonlinear current in azimuthal direction exciting THz electromagnetic fields in the plasma slab. The dependence of the excited radial electric field and azimuthal magnetic field on axial and radial parameters of the plasmas lab, as well as on the slab thickness and laser pulse width size, is investigated. It is demonstrated that the terahertz fields are generated most efficiently with a frequency close to the plasma frequency. It is also shown that the intensity of the excited fields may be optimized and controlled by the plasma slab and laser pulse parameters. Rectangular-triangular, super-Gaussian, and sinusoidal lasers exhibit a significantly steeper radial gradient of ponderomotive potential in comparison with other laser profiles, and excite intense radial electric fields and generate azimuthal magnetic fields in plasma slab. The numerical results closely follow the scaling laws and match with previous experimental and simulation results.