Two charged smoke particles exert a force of 4.2x10^-2 N on each other. What will be the force if they are moved so they are only one eighth as far apart?
F= 4.2x10^-2 N
K= 8.99x10^9
e= 1.6x10^-19
Do I solve for r even though they're asking me to find the force?
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Yes, you need to solve for the distance (r) between the charged smoke particles in order to find the new force when they are moved one eighth as far apart. By applying Coulomb's law, you can find the relationship between the force and the distance.
Coulomb's law states that the force (F) between two charged particles is given by the formula:
F = (K * Q1 * Q2) / r^2
where:
F is the force between the particles,
K is Coulomb's constant (8.99x10^9 N m^2/C^2),
Q1 and Q2 are the charges of the particles, and
r is the distance between the particles.
Since they are asking for the new force, you will solve for the force using the given information.
To find the force when the two charged smoke particles are moved closer together, you can use Coulomb's Law. Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The equation for Coulomb's Law is:
F = (K * |q1| * |q2|) / r^2
Where:
F is the force between the particles
K is Coulomb's constant (8.99x10^9 Nm^2/C^2)
|q1| and |q2| are the magnitudes of the charges on the particles
r is the distance between the particles
Since the force (F) is given as 4.2x10^-2 N, and we are asked to find the new force when the particles are moved closer together, you don't need to solve for r. Instead, you can use the given information and the proportional relationship of Coulomb's Law to find the new force.
Given that the distance between the particles is reduced to one eighth of its initial value, we can say that the new distance (r') is equal to the initial distance (r) divided by 8:
r' = r / 8
Since force (F) is inversely proportional to the square of the distance (r^2), if the distance is reduced to one eighth, the force will increase by a factor of (8)^2 = 64.
Therefore, the new force (F') can be calculated as:
F' = F * 64
Plugging in the given value for F:
F' = 4.2x10^-2 N * 64
Calculating this expression will give you the new force when the particles are moved one eighth as far apart.