Two charges of equal magnitude q are placed in air at a distance 2 a apart and third charge -2q is placed at mid – point. The potential energy of a system is? ( ԑo = permittivity of free space ) . (MHT-CET ~ 2014)

Two charges of equal magnitude q are placed in air at a distance 2 a apart and third charge -2q is placed at mid – point. The potential energy of a system is? ( ԑ_o = permittivity of free space ) . (MHT-CET ~ 2014)

a ] - q ² / ( 8 π ε _o a )                        b] - 3 q ² / ( 8 π ε _o a )                     

c] – 5 q ² / ( 8 π ε _o a )                     d] - 7 q ² / ( 8 π ε _o a )

Solution :

Electric Potential Energy :

The electric potential energy of system of system of point charges can be define as the work required to assemble the system of charges by bringing them from infinite distance to their present location.

U =(1/ 4 π ε _o ) { [ ( q ₁ q ₂  ) / r _{1 2} ] + [ ( q ₁ q ₃ ) /  r _{1 3} ] + [ ( q ₂ q ₃ ) / r _{2 3} ] }

Two charges of equal magnitude q are placed in air at a distance 2 a apart and third charge -2q is placed at mid – point. The potential energy of a system is? ( ԑ_o = permittivity of free space ) . (MHT-CET ~ 2014)

The Electric potential energy of system can be given as

U =(1 / 4 π ε _o ) { [ ( q ₁ q ₂  ) / r _{1 2} ] + [ ( q ₁ q ₃ ) /  r _{1 3} ] + [ ( q ₂ q ₃ ) / r _{2 3} ] }

U = U =(1/ 4 π ε _o ) { [ ( q ₁ (-2q ₁  ) / a ] + [ ( q ₁ (-2q ₁  ) /  a ] + [ ( q ₁ q ₁ ) / 2a ] }

U =(1/ 4 π ε _o ) { - [ (2q ² ) / a ] - [ (2q ² ) / a ] + [ ( q ² ) / 2 a ] }

U =( 1/ 4 π ε _o ) { - [ (4q ² ) ) / a ] - [ (q ² ) ) / 2a ]}

U =( - 7 q ²/ 8 π ε _o a )

The potential energy of system is given by U =( - 7 q ²/ 8 π ε _o a )

The correct option is : option [ d ]