# How many more protons than electrons does the hammer have? What is the charge on the nail? What is the Coulomb force between the hammer and the nail? What would the force be if the hammer were held 7 times farther away from the nail?

## A hammer is charged to 2.21μC and held 0.31m from a nail that has 1.49 x 10^13 more protons than electrons.

May 1, 2017

Elementary charge is =1.602 × 10^-19 " C"

(a) Charge on hammer$= 2.21 \mu \text{C}$
Since the hammer is positively charged it must be electron deficient.
$\therefore$ number of excess protons on the hammer=(2.21xx10^-6)/(1.602 × 10^-19)
$= 1.38 \times {10}^{13}$, rounded to two decimal places.

(b) Number of excess protons on the nail$= 1.49 \times {10}^{14}$
$\therefore$ charge on nail=1.49xx10^14xx1.602 × 10^-19=2.39xx10^-5" C"

(c) From Coulomb's law force between the hammer and nail having charges ${q}_{1}$ and ${q}_{2}$

${F}_{c} = {k}_{e} \frac{{q}_{1} {q}_{2}}{r} ^ 2$
where ${k}_{e}$ is Coulomb's constant = 8.99×10^9 " Nm"^2 "C"^-2, and scalar $r$ is the distance between two charges.

:.F_c=8.99×10^9xx(2.21xx10^-6xx2.39xx10^-5)/r^2
$\implies {F}_{c} = \frac{0.47}{r} ^ 2 \text{ N}$

(d) New distance is $= 7 r$
Due to inverse square nature of Coulomb's force, new force will be

$= {F}_{c} / 49 \text{ N}$
where ${F}_{c}$ is as calculated in (c) above.