Question

Which results in a larger attractive force on a single electron:+3C of charge1.0 m away,or +6c of charge 2 m away?Numerically justify your response?

Answer 1

`e_1=3 C`
`e_2=6 C=2*e_1`
`l_1=1 m`
`l_2=2 m=2*l_1`

`F_1>F_2`

Explanation:

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`