Question 22

[klee92181]

I still do not understand why the answer is zero for this question:

A point charge q at point a was moved to point b with a force F. Points a and b are a distance r from charge Q. What is the work done in moving q from point a to point b?

Work= Fd and F is given, so isn't d the distance that the charge moves, which is 1/2(2pieR), giving W=FpieR

They used the potential energy between 2 charges equation to solve it Ep = kQq/r but why do you need to use this equation when the F is already given?

They gave this explanation, which I still do not understand:
As a rule, no work is done when a charge is moved along an equipotential surface or line since the force component along the line is zero.

Thanks

[admin]

Imagine moving a book along the surface of a table and then being asked how much work was done by gravity? None, of course. In fact, even if the book fell to the floor and then was returned to the same surface: the work done by gravity, dependent on the displacement d not simply the distance, would indeed be zero. It is the same with movement along equipotential lines.

Note the relationship between work done and potential difference:

http://www.physics.fsu.edu/users/ng/courses/phy2054c/Labs/Expt01/Expt-01.htm

http://regentsprep.org/Regents/physics/phys03/aequilines/default.htm

[ajavedx3842]

True, but in your example using a book on a table, it is gravity that does no work on the book, it is your applied force that does the work.

In the question, it says what is the "work done in moving the charge...". Since it says that there was a force applied (F), does this not mean that there was work done by the Force?

If it is on an equipotential, which it is, there should be no force required in moving the charge at all.

See, you use U = kqQ/r , and since none of these values change, yes there is no delta U, therefore no change in energy, and by the work/energy theorem, no net work done...but it seems to me that this greatly conflicts with the wording of the question in which a force is clearly applied, and a displacement clearly observed..

I mean, if there is force applied over distance and it causes a change in the position of an object (but no change in energy), should we always assume that no work is done?

I will have to read on this

[admin]

Perhaps the development and equation in the link below will help since it underlines the importance of the final and initial positions of the charge. In other words, the force can act over a distance along ANY path but if the final and initial positions of the charge lie along an equipotential line then, the conclusion from physics, is there is no work done:

www4.ncsu.edu/~mowat/H&M_WebSite/ElectricFields/FieldsAndPotentials.html

[andrew.bra3483]

If I move a charge along an equipotential line, no work is done.

I have a table which stands at a uniform height above the ground. Its surface is at uniform gravitational potential energy. Suppose I push my book a short distance backwards on my table. Haven't I done work, even though the book's potential energy is unchanged?

Why is my book different from the point charge?

The only difference I discern is that friction resisted the movement of my book, whereas the point charge moves pretty much without resistance or friction opposing it.

[nedaa.asba6809]

What you really should keep in mind is applying force does not imply that work is done.
The relation between kinetic energy and work is that the work done on an object by a net force equals the change in kinetic energy of the object.
Now if the change is done on an equipotential surface the work done is equal to zero.

In the example of the book moving on the table, both the positions of the book (the initial and the final positions) are in the same plane, that is to say that the direction of the force and movement are horizontal to the plane of the table but the whole table plane is perpendicular to the earth gravity plane. Applying the equation to calculate the work [w = F. D =FD cos θ] the angle is between both planes (θ = 90o). Hence the work is equal to zero.

[admin]

Bump.

[RichardParker]

Won't the question make more sense if it read "What is the work done by the Electric Field in moving q from point a to point b?