Abstract:

For uniformly charged hemispheroid，the distribution of the electric field strength on its axis cannot be calculated by the Gauss law because the charge distribution is not highly geometrical symmetry. Based on the superposition principle of electric field strength and the method of electric potential gradient，the analytical solutions of electric field strengths distribution on its axis is derived strictly，the results show that the analytical solutions of the electric field strengths distribution in each region of the axis of the uniformly charged hemispheroid are different，the same conclusions are obtained by various methods. For the charged body with uniform and symmetrical distribution，it is easier to select the appropriate charge element and use the superposition principle of field strength to solve the field strength distribution，while the potential gradient can be used to solve the non-uniform and symmetrical distribution when it is difficult to solve by the superposition principle.

Key words: electric field strengths distribution, uniformly charged hemispheroid, superposition method, electric potential gradient, analytical solution