Answer to Question #79028 in Electricity and Magnetism for Karen

Question

Two objects are separated by a distance of 1.2 mm. The objects are initially neutral, and then each receive the same number of electrons, giving them the same charge. The force between the objects is now 24.0 pN. How many electrons did the two objects each receive?

Answer 1

Let’s first find the charge of each object from the Coulomb’s Law:
F=k (q_1 q_2)/r^2 =k q^2/r^2 ,
q=√((Fr^2)/k)=√((24.0∙〖10〗^(-12) N∙(1.2∙〖10〗^(-3) m)^2)/(9.0∙〖10〗^9 (Nm^2)/C^2 ))=6.2∙〖10〗^(-14) C.
Finally, we can find the number of electrons that the two objects each receive from the equation:
q=Ne,
N=q/e=(6.2∙〖10〗^(-14) C)/(1.6∙〖10〗^(-19) C)=3.875∙〖10〗^5 electrons.