In the experimental setup represented above, a very small plastic sphere of mass

Question

In the experimental setup represented above, a very small plastic sphere of mass m with charge q is allowed to fall under the influence of gravity between two parallel metal plates separated by a fixed distance L. A variable potential difference may be applied between the two plates. The experiment is conducted inside a vacuum chamber. A potential difference of magnitude V is applied between the top and bottom plates such that the sphere falls at a constant speed v. Derive an expression for the magnitude of the charge q on the sphere. Express your answer in terms of m, L, V, and fundamental constants, as appropriate. The experiment is performed many times with spheres of identical known mass but difference unknown charges, each time adjusting the potential difference V to the value needed so that the sphere falls at constant speed v. The magnitudes of the charges are calculated from the measured values of the potential difference. The data is plotted below as a function of the magnitude of V. Provide a physical explanation for the gap observed in the data between potential differences of 1700 V and 2800 V.

Explanation / Answer

The Electric field between the plates is given by :

E = V/L

So, electric force on the charge, Fe = E*q = Vq/L

For constant speed, the net force must be 0

So, that to happed, Fe = Fg

where Fg = force of gravity = m*g

mg = Vq/L

So, q = mgL/V <-------answer

b)

We observe that at V = 1700 V, the charge = 3.2*10^-19 C = twice the fundamental charge

fundamental charge = charge of electron or proton = 1.6*10^-6

Similarly upto V = 2800 V at which charge = 1.6*10^-19 C

This just proves that the 1.6*10^-19 is the fundamental charge

Thus there are no points between 1e and 2e

where e = 1.6*10^-19 C

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---