A pendulum, suspended at the origin, consists of two non- conducting massless ro

Question

A pendulum, suspended at the origin, consists of two non-
conducting massless rods rigidly connected to each other at

the right angle at the center of the lower rod. The lower rod

has two small metal spheres rigidly attached to it at the ends.

The distance between the centers of those spheres is d . The

length of the vertical rod isL and it is much larger than d .

The total mass of both spheres is m . Gravity acts vertically

against y-axis. External uniform electric field is applied

parallel to the x-axis. Spheres have no excess charges

(initially).

(a) if external uniform electric field, of magnitude E0, is

applied against x-axis, and the spheres are briefly connected

by a short small metal wire (along the rod), what will the

resulting distribution of charges be (qualitatively)? How does

it change when the wire connector is being removed? How

does it change if electric field is turned off after the wire was

removed? [2 pts.]

Now, assume that the procedure of (a) is performed. After

that an external uniform electric field is applied along the

x-axis.

(b) Find the period T of small osculations about the

equilibrium position as a function of all relevant parameters.

Can the frequency omega of small oscillations vanish? If so what

does this mean? [5 pts.]

(c) What happens when electric field E becomes very strong.

Find the equilibrium position and the period of small

oscillations in this case [3 pts.]

(d) How to measure/calculate the values of all charges and

the magnitude of , by measuring period of small

oscillations for known . Provide the relation between E0

and charges as the part of your answer. [5 pts.]

Explanation / Answer

a)when connected two spheres with a connector charge will distributed equally.when connector removed charge will be same. If E0 is zero,charges are moving in random motion net charge will be zero.In above case charges are moving with drift velocity in right direction.

if E0 is along x- axis charges are drifted in left direction

b)T=2*pi*sqrt(L/g).if w vanish T=0

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