Item 9
A small glass bead has been charged to 20
Part A -
What is the magnitude of the acceleration of a proton that is 4.0 from the center of the bead?
Express your answer using two significant figures.
=
Part B -
What is the direction of the acceleration of a proton that is 4.0 from the center of the bead?
toward the bead
away from the bead
Part C -
What is the magnitude of the acceleration of an electron that is 4.0 from the center of the bead?
Express your answer using two significant figures.
=
Part D -
What is the direction of the acceleration of an electron that is 4.0 from the center of the bead?
toward the bead
away from the bead
To calculate the magnitude of the acceleration of a charged particle at a distance from a small glass bead, we can use the formula for the electric field due to a charged point object:
Electric Field (E) = k * (q / r^2)
where k is the electrostatic constant (9 * 10^9 N * m^2 / C^2), q is the charge of the bead, and r is the distance from the center of the bead.
In this case, the bead has been charged to 20, so q = 20 * 10^-9 C.
For Part A, we need to find the magnitude of the acceleration of a proton at a distance of 4.0 cm from the center of the bead.
First, we need to find the electric field at that distance:
E = k * (q / r^2)
E_proton = (9 * 10^9 N * m^2 / C^2) * (20 * 10^-9 C / (0.04 m)^2)
Next, we need to use Newton's second law, which states that F = ma, where F is the force on the proton, m is its mass, and a is its acceleration.
Since the force is the electric force between the proton and the bead, we can use Coulomb's law:
F = k * (q_1 * q_2) / r^2
where q_1 and q_2 are the charges of the proton and the bead, respectively.
So, the acceleration can be calculated as:
a_proton = F_proton / m_proton = (k * (q_1 * q_2) / r^2) / m_proton
Given that the proton has a mass of approximately 1.67 * 10^-27 kg, we can substitute the values into the formula to calculate the acceleration:
a_proton = ((9 * 10^9 N * m^2 / C^2) * (20 * 10^-9 C * 20 * 10^-9 C) / (0.04 m)^2) / (1.67 * 10^-27 kg)
Using a calculator, this can be solved to obtain the magnitude of the acceleration of the proton. Remember to express the answer using two significant figures.
For Part B, since the proton has a positive charge, it will be accelerated toward the bead.
Similarly, for Part C and D, we can use the same equations and approach to calculate the magnitude and direction of the acceleration of an electron at a distance of 4.0 cm from the center of the bead. The only difference is that the charge of an electron is -1.6 * 10^-19 C.
Hope this helps!