D) T1 - T2 = m1g + qE1 = m2g - qE2 Solving Magnetism Question Homework

[science.girl]

Homework Statement

Two small objects, labeled 1 and 2 in the diagram (see link), are suspended in equilibrium from strings of length L. Each object has mass m and charge +Q. Assume that the strings have negligible mass and are insulating and electrically neutral. Express all algebraic answers in terms of m, L, Q, q , and fundamental constants.

(a) On the following diagram, sketch lines to illustrate a 2-dimensional view of the net electric field due to the two objects in the region enclosed by the dashed lines.

(b) Derive an expression for the electric potential at point A, shown in the diagram at the top of the page, which is midway between the charged objects.

(c) On the following diagram of object 1, draw and label vectors to represent the forces on the object.

(d) Using the conditions of equilibrium, write—but do not solve—two equations that could, together, be solved for q and the tension T in the left-hand string.

Homework Equations

Please see link for diagrams on page 7: http://apcentral.collegeboard.com/apc/public/repository/ap09_frq_physics_b.pdf

The Attempt at a Solution

For the diagram in part (a), there are two objects with charge +Q. Therefore, the electric field lines would be directed away from one another because the objects repel, correct? Much like this: http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter23/Chapter2326.gif

B) Electric potential? as in V = k_eq/r?
V = (9.0*10^9 N*m^2/C^2)(+Q)/(Lsin$$\theta$$) ??

C) Would forces include: tension from the string, gravity, magnetic force from particle 2?

 

[rl.bhat]

A, B and C are right.

 

[Avodyne]

No, B is wrong; that's the potential from one of the charges. And for C it's electric, not magnetic, forces that are relevant.

 

[science.girl]

No, B is wrong; that's the potential from one of the charges. And for C it's electric, not magnetic, forces that are relevant.

B) So, for the potential from both charges, would I use F = k_e(q1*q2)/r^2? (Edit: Oh wait... this isn't measuring potential, is it?)

C) Would you mind elaborating just a little bit? I think I understand what you're saying.

 

[science.girl]

If someone could please help me with B and D, I would appreciate it.
(I think I got the rest.)

 

[Redbelly98]

(B) Find the potential due to each charge separately.

(D) One of Newton's laws of motion will help here.

 

[science.girl]

(B) Find the potential due to each charge separately.

(D) One of Newton's laws of motion will help here.

B) Still thinking about what equation to use... (V = k_eq/r for each? Because the other equations I've come across are Coulomb's Law [electric force], E = F/q [electric field], E= k_e*q/r^2, and some equations on electric flux.)

D) Oh! F = ma.
But I never applied that equation to an equilibrium problem for something like this. What I would need is two equations that I've encountered, solving one for q and one for T.. Or two equations that would cancel to produce those results?

 

[Redbelly98]

B) Still thinking about what equation to use... (V = k_eq/r for each?

Yes, that's the one

D) Oh! F = ma.
But I never applied that equation to an equilibrium problem for something like this. What I would need is two equations that I've encountered, solving one for q and one for T.. Or two equations that would cancel to produce those results?

Yes, two equations are required.

From a freebody diagram showing all forces acting on one of the charges, you can get an equation for the net horizontal force and also an equation for the net vertical force ... that's two equations, as needed.

 

[science.girl]

Thanks for your help!