Electrostatic Potential and Capacitance Class 12 Physics - Electrostatics of Conductors
The substances that allows flow of current through them are conductors. A conductor is characterised by presence of free movable charge carriers, in case of metal these are electrons, while in case of electrolyte these are positive and negative ions. In metallic conductors, the drifting is influenced by external electric field, while in case of electrolytes, it is influenced by external electric field as well as chemical forces. We will restrict our discussion to metallic conductors.
When a metallic conductor, say a metallic plate, is placed in an electrostatic field. The free electrons within the sheet undergo drift due to the force exerted by field. If the field is directing left to right, then electrons start accumulating on the right side and other side becomes positively charged. Such redistribution of electrons, causes development of internal electric field which is opposite to that of applied electric field. At equilibrium condition, when internal electric field becomes equal to external electric field, the field inside the sheet reduces to zero. Thus, electric field inside the conductor placed in external electric field is zero.
At the surface of the charged conductor, electrostatic field must be normal to the surface at every point.
Suppose, the electric field is at some angle other than 90° with the surface of the charged conductor, then the electric field vector must have two components at point of contact, one perpendicular to the surface, and other parallel to the surface. Definitely the parallel component would have exerted force on the charge residing on the surface and causes them to move, causing surface current. But there is no surface current in electrostatics, hence the tangential component is always zero and the electric field is always perpendicular to the surface.
The interior of a conductor can have no excess charge in the static situation
Think about neutral conductor. There are equal amount of positive and negative charges in every small volume of surface element. For a charged conductor, excess charges reside only on the surface in static situation. This can be explained with the help of Gauss’s law. Consider any arbitrary volume element Δv inside a conductor. Consider a Gaussian surface ΔS, bounding the volume element Δv. We know that electrostatic field is zero inside the conductor. Clearly, the total electric flux through ΔS is zero. Hence, by Gauss’s law, if flux through any closed area is zero then there is no charge inside the area and thus ΔS does not enclose any excess charge.
Electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface.
Since electric field inside the conductor is zero, “E=0”. Therefore no work is done, for bringing the test charge from one point to other inside the conductor. Also, there is no tangential component of electric field on surface hence here also, there is no work done in moving test charge. That means there is no potential difference between two points, present inside the conductor or on surface of conductor.
Electric field at the surface of a charged conductor is
Where σ is the surface charge density and is a unit vector normal to the surface in the outward direction. We already proved this result while studying Gauss Law and its applications.
Electrostatic Shielding
For a charged conductor the electric field inside the cavity is always zero, this is called electrostatic shielding. The shape of the conductor and cavity could be varying but still the result is valid. The proof of this result can be given on the basis of the fact that, for a charged conductor, charges reside on the outer surface of the cavity and no charge exists inside. This effect is applied for protection of the inside from outside electrical influence.
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