This paper presents a study on the analysis and evaluation for ELF( Extremely Low Frequency) electric and magnetic fields under the transmission line according to the power system states. The power system states are classified into two types, normal state resulting from normal operation and alert state from outages. The current in a system is changed continually owing to the load fluctuations even in a normal operation. To calculate the current of the concerned line in a normal state, the system load level is devided into light, base and heavy load level. In case of contingency, an efficient algorithm based on matrix inversion lemma is developed to figure out the current changes. In order to analyze the variations of ELF field caused by the current fluctuations the electrostatic field approach which is far simpler than the electromagnetic field one based on Maxwell equation is introduced in this paper. The suggested method is applied to the IEEE 14 bus system to demonstrate the usefulness.