Question

The electric force between a charged foam cup and a positively charged metal sphere is 2.12 newtons. If the charge on the cup is 2.0 × 10-6 coulombs and the charge on the metal sphere is 2.5 × 10-6 coulombs, what is the distance between the two? (k = 9.0 × 109 newton·meter2/coulombs2.

Answer 1

Using the formula:

F = k.q1.q2/r2 

Manipulating for r.

r = √(Kq1q2/F) 

r = 1.5 x 10^-2 meters 

Answer 2

Answer : The distance between the cup and metal sphere is 0.1457 meter.

Solution : Given,

Charge on the cup = $2.0\times 10^{-6}coulombs$

Charge on metal = $2.5\times 10^{-6}coulombs$

Electric force = 2.12 Newton

coulombs constant, K = $9.0\times 10^9Nm^2/coulombs^2$

Formula used : According to the Coulombs Law,

$F=K_e\times \frac{q_1q_2}{r^2}$

where,

F = Electric force

$K_e$ = coulombs constant

$q_1$ = Charge on the cup

$q_2$ = Charge on the metal

r = Distance between the two charged species

Now put all the given values in above formula, we get

$2.12N=9.0\times 10^9Nm^2/coulombs^2\times \frac{(2.0\times 10^{-6}coulombs)\times (2.0\times 10^{-6}coulombs)}{r^2}$

By rearranging the terms, we get the value of 'r'

r = 0.1457 meter

Therefore, the distance between the cup and metal sphere is 0.1457 meter.