We know that the Electro static potentialJust as above we defne vector magnetic potential We know that 12Substitute1 in 2The vector identityDerivation of Boit-SavartsLaw!"Substitute " in !#Substitute # in$The vector identityWe know thatWe know thatSubstitutee%n&!in e%n& &&"Derivation of Amperes Circuital Law12Substitutee%n&2in e%n&1&&!We know thatWe know that&Substitutee%nin e%n&" &&$Substitutee%n&' in e%n&$ &&'(y using stokes theoremWe know thatSubstitutee%n&2in e%n&112We know that&!Substitutee%n&!in e%n&&"The vector identityWe know that#$Substitutee%n&$ in e%n'We know thatSubstitutee%n&)in e%n&' &&1*&&)We know that&&11We know thatSubstitutee%n&11in e%n&1* &&12Substitutee%n&1 in e%n&12 &&1&&1!Let us now consider the force between two elements and According to Biot-Savart's law, both current elements produce magnetic fields.So the force on element due to the field produced by element The total +orce on current loop 1 de to current loop 2