Biot's Experiments , Faradays's Ice Pail Experiment and Surface Density of Charge

Biot's Experiment

A charged metal sphere C is taken which is fitted on an insulating stand. Then take two metallic hemispheres A and B which exactly fit on the sphere C and are provided with insulating handles as shown in the figure. Bring hemispheres A and B near so that they can enclose the sphere C. Remove the hemispheres. Test the charge of C. Now you can see C does not possess any charge. It's charged has been transferred to the outer surface of two hemisphere A and B. This experiment shows that charge reside on the outer surface of a conductor.

Faraday's Ice-Pail Experiment

Faraday devised the following two experiments

Experiment 1:

• Take a metallic vessel and place it on the disc of GLE. Since the vessel is electrically neutral, the gold leaves do not diverge.
• A positively charged metallic sphere is taken and suspended by a silk thread.
• The sphere is lowered gradually into the ice pail without touching it. The divergence of the gold leaves goes on increasing and becomes maximum when the sphere is completely inside the ice pail.
• Metallic sphere is gradually removed from the ice pail without touching its wall, the divergence of the gold leaves collapses.

This means the induced negative charge on the inner side of ice pail due to electrostatic induction on the wall are cancelled by the induced positive charge on the outer side of the ice pail. It can be concluded that induced negative and positive charge are equal in magnitude.That is,

induced positive charge = induced negative charge.

Experiment 2:

• Lower the positively charged metal sphere again lowered in ice pail. The divergence of the gold leaves goes on increasing and becomes maximum when the sphere is completely inside the ice pail.
• Lower the metal sphere at the bottom of the ice Pail without touching the walls. The sphere does not possess any charge. But leaves remained diverted to their maximum positions as in the figure.

It means the positive charge in the sphere is neutralised by the negative induced charge on the inner wall of ice pail. The divergence is due to the positive charge on the outside of ice pail. It can be concluded that induced negative or positive charge is equal to the inducing charge.

That is,

induced charge = inducing charge.

Surface Density of Charge

The surface density of charge is defined as the amount of charge per unit area of a charged surface. It is denoted by σ.

Of Q is distributed uniformly over the surface area A of a conductor, then the surface density of charge is given by

$$ \sigma = \frac {Q}{A} $$

In S.I units the units of surface density of charge is coulomb meter^-2 (Cm^-2) .

The surface charge density depends upon the shape of the conductor. The surface density at all points of a spherical charge conductor is same as shown in figure.