When sugar is poured from the box into a bowl , the rubbing of the sugar grains create a static charge that repels the grains , and causes the sugar to go flying out in all directions. If each of two grains acquires a charge of 3.0x10^-11 C at a separation of 8.0x10^-5 m, with what force will they repel eachother
force=k(3e-11)^2/(8e-5)^2=9/64 k e-12
k=9e9
force=about 81/64 e-3 N
check that.
To calculate the force with which two charged grains repel each other, you can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is:
F = (k * q₁ * q₂) / r²
where:
F is the force between the charges,
k is Coulomb's constant (approximately 9.0 x 10^9 N*m²/C²),
q₁ and q₂ are the charges of the grains, and
r is the separation distance between the grains.
In this case, the charges are given as 3.0 x 10^-11 C each, and the separation distance is 8.0 x 10^-5 m. Plugging these values into the formula, we get:
F = (9.0 x 10^9 N*m²/C²) * (3.0 x 10^-11 C) * (3.0 x 10^-11 C) / (8.0 x 10^-5 m)²
Simplifying this expression, we have:
F = (9.0 x 10^9 N*m²/C²) * (9.0 x 10^-22 C²) / (6.4 x 10^-9 m²)
F = 81 x 10^-13 N / (6.4 x 10^-9 m²)
F ≈ 1.266 x 10^-4 N
Therefore, the force with which the two charged grains repel each other is approximately 1.266 x 10^-4 Newtons.