AnswerSolving Electrostatic Force: Find Charge & Mass

[nic4birds]

electrostatic force?

Homework Statement

Two very small spheres are initially neutral and separated by a distance of 0.50 m. Suppose that 6.2 x 1013 electrons are removed from one sphere and placed on the other. What is the magnitude of the electrostatic force that acts on each sphere?,

Homework Equations

Each electron carries an amount of charge with magnitude e=1.6*10^-19

Homework Statement

Homework Statement

Q2. Two particles, with identical positive charges and a separation of 3.80 x 10-2 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1 whose magnitude is 6.71 x 103 m/s2, while particle 2 has an acceleration a2 whose magnitude is 9.64 x 103 m/s2. Particle 1 has a mass of 7.46 x 10-6 kg. Find (a) the charge on each particle and (b) the mass of particle 2.

Homework Equations

F=kq1q2/r^2

 

[Kurdt]

Where are your attempts at the solution for both of these problems?

 

[nlightner]

a1=q1/m1
a2=q2/m2
F=ma

The electrostatic force between two charged particles is given by Coulomb's Law: F = kq1q2/r^2, where k is the Coulomb constant, q1 and q2 are the charges on the particles, and r is the distance between them.

For the first problem, we can use Coulomb's Law to calculate the electrostatic force between the two spheres. Since one sphere has gained 6.2 x 1013 electrons, it now has a net charge of -6.2 x 1013e. The other sphere has lost 6.2 x 1013 electrons, giving it a net charge of +6.2 x 1013e. Plugging these values into the equation, we get:

F = (9 x 109 N·m2/C2)(-6.2 x 1013e)(6.2 x 1013e)/(0.5m)2
= -1.84 x 10-6 N

Since the electrostatic force is a vector quantity, it acts in the opposite direction on each sphere. Therefore, the magnitude of the force acting on each sphere is 1.84 x 10-6 N.

For the second problem, we can use the given acceleration values and equations for electrostatic force and acceleration to find the charge and mass of each particle. First, we set up a system of equations:

F = kq1q2/r^2
a1 = q1/m1
a2 = q2/m2

We can rearrange the first equation to solve for q1:

q1 = (Fm1r^2)/(kq2)

Then, we substitute this into the second equation to solve for q2:

a2 = (Fm1r^2)/(kq2m1)

Finally, we substitute the given values and solve for q2:

q2 = (Fm1r^2)/(a2m1k)
= [(9 x 109 N·m2/C2)(7.46 x 10-6 kg)(3.8 x 10-2 m)2]/(9.64 x 103 m/s2)(7.46 x 10-6 kg)(9 x 109 N·m2/C2)
= 1.44 x 10-19