Two electrons repel each other with a force that varies inversely as the square of the distance between them, where k is the constant of proportionality. One electron is fixed at the point . Find the work done in moving the second electron from to .
A) units of work
B) units of work
C) units of work
D) units of work
E) units of work

Question

Two electrons repel each other with a force that varies inversely as the square of the distance between them, where k is the constant of proportionality. One electron is fixed at the point  . Find the work done in moving the second electron from  to  .
A) units of work 
B) units of work 
C) units of work 
D) units of work 
E) units of work

Quizplus · Accepted Answer

The force between the two electrons can be expressed as:

F = k(q1q2/r^2)

where q1 and q2 are the charges of the two electrons, r is the distance between them, and k is the Coulomb constant.

Since each electron has the same charge, we can simplify the equation to:

F = k(q^2/r^2)

where q is the charge of each electron.

To find the work done in moving the second electron from point A to point B, we need to integrate the force over the distance:

W = ∫Fdx = ∫k(q^2/x^2)dx

where x is the distance between the two electrons.

Integrating this expression yields:

W = -kq^2(1/x)|A to B

Plugging in the given values of point A and point B, we get:

W = -kq^2(1/10 - 1/13)

W = kq^2(1/13 - 1/10)

W = kq^2(3/130)

Since we are only interested in the units of work, we can ignore the constant k and the charge q, and we are left with:

W = 3/130 units of work

Converting to the given format, the answer is:

Answer: D

Two Electrons Repel Each Other with a Force That Varies