Question

how does magnetic force in one frame is converted into electric force in other

Answer 1

\(\huge gradient\space\space X \vec E=-{\partial\vec B \over \partial t}\)
\(\huge gradient\space\space X \vec B=\mu_0 j+\epsilon_0 \mu_0 {\partial\vec E \over \partial t}\)

Answer 2

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html

Answer 3

actually the question should have been why is magnetic FIELD in one frame convert to an electric field in a moving frame. For example an electron stationary in a magnetic filed feels no force. Only as it moves relative to the field does it experience a force. Maxwell's equations govern this behavior.