91Ó°ÊÓ

The given data can be listed below as,

• The changed value of the distance is, ${\mathrm{d}}_1=2\mathrm{d}$.
• The magnitude of new point charge is +3Q.
• The magnitude of another new changed point charge is -2Q.

Whenever the interaction of a specific point charge with an electric dipole occurs, there would be an electric force due to the electric dipole acting on the point charge.

The electric field due to the dipole at the location of the point charge points in the -x direction and the expression of the dipole exerts a force on toward the dipole can be expressed as,

Here,$\stackrel{→}{\mathrm{F}}$ represents the dipole exerts a force on Q toward the dipole,$\stackrel{→}{\mathrm{E}}$ represents the electric field due to the dipole at the location of the point charge points in the -x direction,${\mathrm{Î\mu }}_0$ represents the vacuum permittivity.

Now since the distance doubles then the expression of the dipole exerts a force on Q toward the dipole can be expressed as,

Here,$\stackrel{→}{{\mathrm{F}}_1}$ represents the dipole exerts a force on Q toward the dipole due to double the distance d.

Substitute all the values in the above equation.

Hence, the electric force on the point charge due to the dipole reduced by a factor equal to $\frac{1}{8}$.

Now since the magnitude of the point charge changes to +3Q then the expression of the dipole exerts a force on +3Q toward the dipole can be expressed as,

Here, $\stackrel{→}{{\mathrm{F}}_2}$represents the dipole exerts a force on +3Q toward the dipole.

On solving the equation (1) and equation (2) we get:

Hence, the factor by which the electric force changes if the point charge has a charge of +3Q is 3.

Now since the magnitude of the point charge changes to -2Q then the expression of the dipole exerts a force on -2Q toward the dipole can be expressed as,

Here,$\stackrel{→}{{\mathrm{F}}_3}$ represents the dipole exerts a force on -2Q toward the dipole.

On solving the equation (1) and equation (3) we get:

Hence, the factor by which the magnitude of the electric force changes if the point charge has a charge of -2Q is 2.