The force can be written as: #vecF=e vecE#, where is
#e#- test charge (in your case #e_0#)
#vec E#- electric field generated by other charges.
#vec E# of a point charge is #vec E=e/(4*pi*epsilon_0*r^2) vec r/r# where:
#r#- vector's length
#epsilon_0=8.85*10^(-12) (As)/(Vm)#
Your exercise is 1D #=># 1D vectors are just numbers.
#E_1=e_1/(4*pi*epsilon_0*l_1^2)=2.7*10^(10) V/m#
#E_2=e_2/(4*pi*epsilon_0*l_2^2)=#
#=(2*e_1)/(4*pi*epsilon_0*(2*l_1)^2)=#
#=(2*e_1)/(4*pi*epsilon_0*4*l_1^2)=#
#=(e_1)/(4*pi*epsilon_0*color(red)( 2)*l_1^2)=#
#=E_1/2=1.35*10^(10) V/m#
#F_1=e_0*E_1=1.6*10^(-19)As*2.7*10^(10) V/m=4.32 N#
#F_2=e_0*E_2=1.6*10^(-19)As*1.35*10^(10) V/m=2.16 N#
#E_1>E_2# #=># #F_1>F_2#
Remember: #J=N m=V A s#
