How to solve

Use, when needed, $K=9{10}^9$ and $e=1\mathrm{.}6{10}^{-19}C$

Exercise $1$:

Two conducting identical spheres A and B $,$ of respective charges $q_A=-1\mathrm{.}5{10}^{-9}C$ and $q_B=4\mathrm{.}5{10}^{-9}C,$ are separated by a distance $d=30cm.$

$1.$

$1\mathrm{.}1.$ Sphere A has excess in electrons. Why?

$1\mathrm{.}2.$ Calculate the number of these electrons.

$1\mathrm{.}3.$ Write the characteristics of the force of the electrostatic interaction exerted by sphere $A$ on $B.$

$2.$ The two spheres are put in contact until electric equilibrium is reached and then separated to the same distance $d=30cm.$

$2\mathrm{.}1.$ Calculate the values $q_A^{\text{'}}$ and $q_B^{\text{'}}$ of the charges of the two spheres after contact.

$2\mathrm{.}2.$ Which sphere has lost electrons?

$2\mathrm{.}3.$ Determine the number of transferred electrons.

$2\mathrm{.}4.$ Calculate the new value of the force of interaction between the two spheres.

$2\mathrm{.}5.$ Is this force repulsive or attractive? Justify.

$3.$ Sphere B is now approached to another sphere D of charge $q_D.$ The distance between the two spheres is $d^{\text{'}}=50cm$ and the electrostatic force between them is repulsive and of magnitude $F^{\text{'}}=1\mathrm{.}35{10}^{-7}N.$

$3\mathrm{.}1.$ Specify the sign of the charge of sphere $D.$

$3\mathrm{.}2.$ Determine $q_D.$