Question

Two very small 8.55-g spheres, 15.0 cm apart from center to center, are charged by adding equal numbers of electrons to each of them.
(a)Disregarding all other forces, how many electrons would you have to add to each sphere so that the two spheres will accelerate at 25.0g when released?
(b)Which way will they accelerate?

Answer 1

Answer:

a) n = 4.77 × 10^7

b) They will accelerate away frpm each other.

Explanation:

a) According to Newton’s Second Law of motion:

   Force of each sphere = (mass)(Acceleration)

   Force of each sphere = (8.55 × 10^-3)(25) =  0.21N

Let Q be the charge on each sphere so, according to coulomb’s Law:

       F = K Q^2/d^2

      Q^2 = (0.21)(15×10^-2)^2/(9×10^9)

      Q^2 = 5.83 × 10^-23

      Q = 7.63 × 10^-12 C

The number of electrons that we have to add can be found using followind formula:

       Q = ne  

       n = 7.63 × 10^-12/e

       n = 4.77 × 10^7

b) As both spheres have electrons (Same charge) so they will accelerate  away from each other.

Answer 2

Answer:

1.43 x 10¹⁷.

They will accelerate away from each other.

Explanation:

Force on each charged sphere F = mass x acceleration

= 8.55 x 10⁻³ x 25 x 9.8

= 2.095 N

Let Q be the charge on each sphere

F = $\frac{9\times10^9\times Q^2}{(15\times10^{-2})^2}$

2.095 =$\frac{9\times10^9\times Q^2}{(15\times10^{-2})^2}$

Q² =$\frac{2.095\times(15)^2\times10^{-4}}{9\times10^9}$

Q = 2.289 X 10⁻⁶

No of electrons = Charge / charge on a single electron

= $\frac{2.289\times10^{-6}}{1.6\times10^{-19}}$

=1.43 x 10¹³.

They will accelerate away from each other.