Electroscope

Scope of the operation of the electroscope

The verserium 1600 from William Gilbert.

The electroscope is an instrument used to read if a body is electrically charged; also in antiquity they saw it in another unidentified way.

The electroscope consists of a vertical metal rod that has a sphere at the top and two sheets of very thin aluminum at the opposite end. The rod is supported on top of a clear glass box with a grounded copper frame. When an electrified object is brought closer to the sphere, the rod becomes electrified and the charged plates with the same sign of electricity repel each other, separating, their divergence being a measure of the amount of charge they have received. The electrostatic repulsive force is balanced by the weight of the sheets. If the object is moved away from the sphere, the sheets, upon losing polarization, return to their normal position.

When an electroscope is charged with a known sign, the type of electric charge of an object can be determined by approximating it to the sphere. If the lamellae separate, it means that the object is charged with the same type of charge as the electroscope. Otherwise, if they come together, the object and the electroscope have opposite signs.

An electroscope gradually loses its charge due to the electrical conductivity of air produced by its ion content. Thus the speed with which an electroscope charges in the presence of an electric field or discharges can be used to measure the density of ions in ambient air. For this reason, the electroscope can be used to measure background radiation in the presence of radioactive materials.

The first known electroscope, the versorium, a pivoting gold-flake electroscope, was invented by William Gilbert in 1600.

Explanation of its operation

An electroscope is a device that allows you to repeatedly raise and lower the charge of a charged object taking advantage of the phenomenon of charge separation by induction.

If we bring a positively charged naked body closer to us, for example a pen that has been rubbed with a cloth, the negative charges in the conductor experience an attractive force towards the pen. For this reason they accumulate in the part closest to it. On the contrary, the positive charges of the conductor experience a repulsive force and for this reason accumulate in the farthest part of the pen.

What has happened is that the charges have moved, but the sum of positive charges is equal to the sum of negative charges. Therefore, the net charge on the conductor remains zero.

Now consider what happens in the electroscope. Remember that an electroscope is essentially made up of a pair of metal sheets joined at one end. For example, a long strip of aluminum foil folded in half.

If we bring the charged pen closer to the electroscope, as indicated in the figure, the negative charge will be attracted to the nearest end of the pen, while the positive charge will accumulate at the other end, that is, it will be distributed among the two sheets of the electroscope.

The situation is shown in the figure: the two free ends of the electroscope were positively charged and since the charges of the same sign reject each other, the leaves of the electroscope separate. If the pen is now moved away, the positive and negative charges of the electroscope are redistributed again, the repulsive force between the blades disappears, and they come together again.

What happens if you touch the end of the electroscope with your finger while it's near the charged pen? The negative charge accumulated at that end "will pass" hand and therefore the electroscope is positively charged. Because of this the sheets do not come together when the pen is moved away.

Determination of the load from the angle of separation of the sheets

Simplified electroscope.

A simplified electroscope model consists of two small m-mass spheres loaded with equal loads q and the same sign that hangs from two threads in length las indicated if the figure. From the angle measurement θ θ {displaystyle theta } which forms a sphere with the vertical, can calculate its load q.

Three forces act on each sphere: the weight mg, the tension in the string T and the electrical repulsion force between the little balls F.

In equilibrium:

(1)Twithout θ θ =F{displaystyle T sin theta =F,!}

(2)T# θ θ =mg{displaystyle T cos theta =mg,!}

Dividing (1) by (2) member by member, we get:

without θ θ # θ θ =Fmg⇒ ⇒ F=mg.So... θ θ {displaystyle {frac {sin theta }{cos theta }}}={frac {F}{mg}}Rightarrow F=mg.tan theta ,!}

By measuring the angle, the repulsive force F between the two charged spheres is obtained from the previous formula.

According to the Coulomb Act, as q1=q2{displaystyle q_{1}=q_{2},!} and

r=2lwithout θ θ ⇒ ⇒ F=q24π π ε ε 0(2lwithout θ θ )2{displaystyle r=2lsin theta ,!Rightarrow F={frac {q^{2}{4pi epsilon _{0}(2lsin theta)^{2}}}}}}}}}}

So, like l{displaystyle l,!} is known and F{displaystyle F,!} has been calculated, clearing q{displaystyle q,!} is obtained:

q=F4π π ε ε 0(2lwithout θ θ )2=4lwithout θ θ π π ε ε 0mgSo... θ θ {displaystyle q={sqrt {F4pi epsilon _{0}(2lsin theta)^{2}}}}}=4lsin theta {sqrt {pi epsilon _{0}mgtan theta }}}}}}}

The usefulness of the electroscope to determine the presence of electric charges and their sign (+ -) is then demonstrated.