Shielding

Shielding is an important concept of Physics. It is the process of limiting the electric field to a certain region of space. Sometimes it is also referred to as screening. An earthed conductor will act as a screen or a shield against the electric field. By placing a metal screen PQ near a charged body B, the resultant electrostatic field due to the electrostatic induction is shown in the figure below. But when the conductor PQ is earthed, then the free induced positive charge on it flows to the earth. Further, it disappears the lines of force emanating from it and it is shown in figure-b.

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Conductors Without Cavity

Good electrical conductor like copper contains charges that are not bound to any atom. These are free to move about within the material. When there is no net motion of charge within the conductor, then the conductor is having electrostatic equilibrium. A conductor in electrostatic equilibrium will show the following properties.

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1. The electric field will always be zero everywhere inside the conductor. It is a fact that induced charges appearing on the surfaces are equal and opposite.

2. The electric field must be normal at every point to the surface of the charged conductor.

3. Any charge on an isolated conductor resides on its surface. Consider a Gaussian surface inside the charged conductor carrying charge q. Since there is no electric field inside the conductor (and hence the Gaussian surface) from Gauss’s law:

\[\int \overrightarrow{E}.\overrightarrow{ds} = \frac{q}{\epsilon _{0}}\]

Thus q =0, for E = 0.

Thus, there is no charge inside the conductor and the excess charge q resides on its surface. However, Gauss’s law does not tell us how this charge is distributed on the surface. This principle that there are no charges on the inner surface of a charged body, can be used to transfer the charge from a sphere to a previously charged conductor.

4. The electric field just outside a charged conductor has a magnitude \[\frac{\sigma }{\epsilon _{0}}\]  . 

Here, we know that \[\sigma\] is the charge per unit area at that point.

Applying Gauss’s law to this surface, we get,

E = \[\frac{\sigma }{\epsilon _{0}}\]

or, with a normal vector with the surface inclusion, we get,

E = \[\frac{\sigma }{\epsilon _{0}}\]  \[\hat{n}\]

Here, \[\hat{n}\]  is a unit vector normal to the surface in the outward direction.

It must be noted that the above Equation is true for both signs of σ. Also, this equation agrees with the results already obtained and is known as coulomb’s theorem.

Conductors with Cavity

Consider a conductor of arbitrary shape containing a cavity as shown in the figure.

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The electric field within the cavity will be zero, irrespective of the charge distribution on the outside surface of the conductor. Also, the field inside the cavity is zero even if an electric field exists outside the conductor. 

Now imagine that a field \[\overrightarrow{E}\] exists in the cavity, and then we evaluate the potential difference means (VQ - VP), which is given as:

VQ - VP = - \[\int \overrightarrow{E}. \overrightarrow{dl}\]   

We must remember that a cavity surrounded by the conducting walls is a field-free region, till there are no charges inside the cavity.

Electrostatic Potential

The electrostatic potential will be constant throughout the volume of the conductor and will have the same value (as inside it) on its surface. So, there is no potential difference between any two points that may be inside or on the surface of the conductor. In case, the conductor is charged, the electric field normal to the surface exists which means the potential is different for the surface and a point outside the surface.

Distribution of Charges on the Conductors

The distribution of charge on the surface of a conductor can be evaluated by the surface charge density \[(\sigma )\] . This density is the charge per unit area of the conductor. So, with the uniformly distributed charge q present on area A, the surface density of charge will be,

\[\sigma\] = q/A

And if with uniformly distributed charge, we have,

\[\sigma\] = \[\frac{\Delta q}{\Delta A}\]

Here, \[\Delta q\] is the amount of charge on a very small \[\Delta A\]

Representation of Surface Density of Charge

The distribution of charge depends upon the shape of the conductor’s surface as well. As we know that,  the surface density of charge is directly proportional to the curvature of it. So, at a point where the conductor has a large curvature, the distance between the points in the conductor is also large. Thus, we can say that, wherever the curvature is uniform, the surface density is also uniform. And also at the edges and corners, the surface density of charge will be maximum. And for sure, there is no charge inside the conductor.

Fun Facts

• The practical application of shielding can be seen in the wire carrying the audio signal from the external electric field.

• A Faraday shield is an enclosure used to block the electromagnetic fields.

• Generally, shielding is achieved by covering the electric field with some non-conductor material.

• Net charge inside the conductor will always remain zero.

• The electric field passes only through the insulator, whereas the conductor simply guides it further.