Electrostatics problem

[kolahal_b]

1]Two small spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x<<l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v=a√x, where a is a constant.

The problem has been done: First we find q2 in equilbm Condition in terms of m, g, l, x etc. Then we differentiate w. r. t. time. dq/dt may be obtained from this. But I wonder why will the charge leakage occur? Which principle results in it and in what way?

[Mercedes Benzene]

Is this a homework problem?

[cwes99_03]

1]Two small spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x<<l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v=a√x, where a is a constant.

The problem has been done: First we find q2 in equilbm Condition in terms of m, g, l, x etc. Then we differentiate w. r. t. time. dq/dt may be obtained from this. But I wonder why will the charge leakage occur? Which principle results in it and in what way?

Charge leakage occurs because there are still forces being exerted on the charges.

In the same way, our atmosphere is slowly leaking into space. While gravity holds it down toward the surface, a small percentage of the gasses in our atmosphere are traveling at a great enough rate to escape the gravitational pull. The warmer the earth gets, the faster some particles move and the more our atmosphere gets boiled off.

 

In the case of the spheres, there are forces of attraction and repulsion, and air is not a perfect insulator (I don't know anything that is.) So given that there are ions in the air (both positive and negative) and these are free to interact with the spheres, some of the charge will be lost when the ions give up or take an electron.

 

Oh, and then you have the effects of the electric fields. Can you calculate how much energy it takes to sustain an electric field on a sphere of metal m which in and of itself has physical properties for how easy it takes and gives up a charge.

[kolahal_b]

I think,charge leakage will occure naturally, as you said.As a result, there will be a less repulsion, so component of tension makes the two spheres closer.As they get closer, charge leakage enhances.I calculated to see that dq/dx is positive i.e. at lower x q will also be lowered.

[Qfwfq]

Charge leakage is the principle of a radiation dosimeter, which is really just a small, highly insulated, quartz fiber electrometer with its own little microscope for reading it, all in a rod the size of a pen that can be clipped to a shirt pocket. It has a system for recharging it to the right voltage, after that the amount of radiation that has been through it can be read as how much the electrometer has discharged.

[cwes99_03]

Of course there you are introducing a high powered charged element that is ionizing the air as it passes by.