Floating Cork Ball - Charge Calculation

[Bailey]

not sure why i keep getting it wrong....maybe caz i misunderstood some concept or something. anhyoo...here is it:

A cork ball of mass 5.20 g is placed between two very large horizontal plates. The bottom plate has a uniform charge density of +0.22E-06 C/m2, whereas the upper plate has a uniform charge density of -0.06E-06 C/m2. The cork ball, which carries an unknown charge, is placed between the plates and is observed to float motionlessly. What is the charge on the ball?


how i plan to solve it: since it give a mass, so i can find the force its acting downward due to gravity, which is "mg".

n since the ball is not moving up or down, there must be a force equal in magnitude but opposite in direction pointing upward). thus the charge of the ball should be positive.

i used E = (surface charge density) / permittivity of free space (8.85x10^-12)

then use F = qE ----> q = F/E

i ended up with 2.01E-16 C ....but its wrong.
anyone know why?

 

[Bailey]

omg.lol. never mind. our prof emailed us witha hint on this question -_-"

the magnitude of the electric field = 1/2(sigma/epsilon)

epsilon = permittivity of free space.

well i ended up with 3.22x10^-6 C , which is correct. (but wasted so much time on it)

 

[wais]

It seems like you have the right approach to solving this problem. However, there may be a few factors that could be causing your incorrect answer. First, make sure you are using the correct units for all of your values. It is important to convert all units to SI units (meters, kilograms, seconds, etc.) before plugging them into any equations.

Another potential issue could be the direction of your forces. Remember that the electric field points from positive to negative charges, so the direction of the force on the cork ball may be different than what you initially thought. Be sure to consider the direction of the electric field in your calculations.

Also, double check your calculations to make sure you are not making any math errors. Sometimes small mistakes in calculations can lead to significantly different answers.

If you are still having trouble, you can try approaching the problem from a different angle. Instead of using the electric field equation, you can also try using the equation for electric force, F = kq1q2/r^2, where k is the Coulomb's constant (8.99x10^9 Nm^2/C^2). Since you know the distance between the plates and the surface charge densities, you can use this equation to find the force on the cork ball and then solve for the unknown charge.

Remember to always check your work and make sure you are understanding the concepts correctly. Good luck!