Electrostatic Shielding

ELECTROSTATIC SHIELDING AND EARTHING OF CONDUCTORS Let's consider a conducting sphere containing a cavity. We denote the surfaces of the cavity and the outer surface of the sphere as S₁ and S₂ respectively. Suppose we introduce a positive charge +Q at Q₁ in this cavity. As a result, negative charge –Q will be induced on the inner surface of the cavity, and positive charge +Q will be induced on the outer surface of the sphere. Consequently, the total charge residing on the inner surface of the cavity is Q₁' = q + Q₁ = -Q. Meanwhile, considering the initial charge Q₀ + Q on the outer surface of the sphere, the total charge on this surface becomes (Q₀ + Q). Considering the spherical nature of the cavity surface S₁, the charge Q₁' will be uniformly distributed across the inner surface of S₂. As a result, the electric field originating from it will be non-zero. The field created by the total charge within the cavity (i.e., Q₁ + Q), becomes nullified. For cavities with arbitrary shapes, Q₁ is distributed non-uniformly across the inner surface. However, for an isolated in a manner that is isolated from electric fields outside the cavity's surface, caused by the total charge within the cavity (i.e., Q₁ + Q), remains zero. As the sphere is conductive, within the material of the sphere (designated as point B), the electric field induced by the charge residing on the outer surface of the sphere is also zero. The electric field at any point outside the sphere, exemplified by a point like C, originates solely from the charge residing on the outer surface of the sphere. Consequently, it can be concluded that the collective charge inside the cavity (i.e., Q₁+Q) holds no influence on the external environment surrounding the surface of the cavity. Conversely, if a charge q is positioned outside S₁, or if an external electric field is established, the charge within the a cavity S remains unaffected by their presence. This characteristic is referred to as "Electrostatic Shielding." This property of a conductive cavity ensures that any charge or device situated inside the cavity remains isolated from external electric fields. It's akin to a car being shielded from lightning strikes. Therefore, during a lightning event, it's safer to decelerate the vehicle and remain inside rather than abandoning it. Considering point B lies within the material of the conductor, the resultant electric field at that point becomes null. Consequently, at this point, the sum of electric fields induced by the charges Q₁, and Q₀ equals zero, denoted as E₀+E₁+E₀=0. Given that the electric field outside surface S₁ results from the total charge within the cavity (i.e., Q₁+Q) is zero. Implying E₀+E₁=0, it follows that E₀= 0. In practical terms, the charge Q₀ situated on the outer surface of the sphere (i.e., S₂) with the cavity adjusts its distribution to ensure that the electric field within S₂ originating from Q₀ remains null across all points. [Image showing a spherical conductor with an inner cavity. A charge +q is inside the cavity. The inner surface is S1 and the outer surface is S2. Points B and C are shown inside the conductor material and outside the sphere, respectively.] [Image showing a solid conducting sphere in an external electric field. A charge +q is inside a cavity within the sphere. Points B and C are also shown.] External electric field (Eₑₓₜ) If a conducting sphere with a cavity is positioned within an external electric field, the resultant electric field at point B is expressed as the sum of the electric fields induced by the charges Q₁, Q₂, and the external field, denoted as E₁+ E₂+ Eₑₓₜ = 0. Given that at point E₀+E₁=0, it follows that E₀= 0. Hence, due to the influence of the external electric field, the charge Q₀ situated on the outer surface of the conducting sphere (cavity) S₂ adjusts its distribution to ensure that the collective electric field within S₂ originating from Q₀ alongside Eₑₓₜ becomes zero. Importantly, the charge within the cavity remains unchanged despite the application of the external electric field. When a charge Q is introduced into the cavity of the conductor, it induces a charge Q1 on the inner surface and further induces a charge Q2 on the outer surface. The combined effect of Q and Q1 results in a net electric field of zero at every point outside the inner surface of the conductor. Similarly, if any charge is positioned outside the conductor or an external electric field is applied, the charge Q2 on the outer surface adjusts its distribution to ensure that the electric field within the conductor, resulting from the combined effect of Q2 and the external field, becomes zero across all points within the material. [Two diagrams showing the distribution of induced charges on a conductor with a cavity, with a positive charge +q inside.] A positive point charge denoted as +Q is placed precisely at the center of a spherical cavity. The negative charge –Q will be uniformly distributed across the inner surface of the cavity, as the cavity wall maintains a spherical shape. Conversely, the positive charge +Q will be uniformly distributed across the outer surface of the conducting sphere. A positive point charge denoted as +Q is placed in an arbitrary position inside the spherical cavity of a spherical conductor. The charge induced on the inner surface of the cavity must be arranged in a manner that cancels out the electric field outside the cavity surface. Consequently, the distribution of induced charge on the inner surface will be non-uniform, as it needs to counteract the external electric field effectively. The positive charge +Q will distribute itself across the outer surface of the conducting sphere. Consequently, the distribution of charge on the outer surface remains constant. Distribution of charge refers to the arrangement or spread of electric charge within a given object or system. In a conductor, charges can redistribute themselves in response to external influences, such as the presence of nearby charged objects or electric fields. This redistribution of charge leads to changes in the electric field both within and around the conductor. Understanding the distribution of charge is essential in various fields, including electrostatics, electronics, and electrical engineering, as it affects the behavior and properties of electrical systems and components. [Image of a conductor with a spherical cavity and a charge +Q at the center.] S₁, S₂ The surface of the cavity, denoted as S₁, possesses a spherical shape. The outer surface of the conductor, represented by S₂, exhibits an arbitrary or non-specific shape. A positive point charge denoted as +Q is positioned precisely at the central point within a spherical cavity. The induced charge distribution on the surface S₁ is uniform, meaning it is evenly spread across the entire surface. The induced charge distribution on the outer surface is not uniform, indicating that it is not evenly distributed across the surface and varies in magnitude or concentration at different points. [Image of a conductor with an arbitrary cavity and a charge +q inside.] S₂, S₁ The surface of the cavity, denoted as S₁, has a spherical shape. The outer surface of the conductor, referred to as S₂, exhibits an arbitrary shape, meaning it does not adhere to a specific or predetermined form. A positive point charge, denoted as +Q, is placed at any location within the spherical cavity, excluding the central point. The distribution of induced charge on surface S₁ is non-uniform, indicating that the charge is not evenly spread across the entire surface and varies in concentration at different points. Similarly, the distribution of induced charge on surface S₂ is also non-uniform, signifying that the charge is not uniformly distributed across the outer surface of the conductor and varies in intensity or density at different locations. [Image of a conductor with a non-spherical cavity and a charge +q inside.] S₁, S₂ The surface of the cavity, denoted as S₁, exhibits an arbitrary shape, meaning it does not adhere to a specific or predetermined form. The outer surface of the conductor. A positive point charge, denoted as +q, is placed at any arbitrary position within the cavity. The distribution of induced charge on the surface S₁ is non-uniform, indicating that the charge is not evenly spread across the entire surface and varies in concentration at different points. referred to as S₂, has a spherical shape, indicating that it is rounded and symmetrical. Conversely, the distribution of induced charge on the surface S₂ is uniform, implying that the charge is evenly spread across the entire surface without variation in concentration. Connecting or touching of conductor Connecting or touching of a conductor refers to the physical contact established between two or more conductive objects or components. This contact allows for the flow of electric charge between the conductors, enabling the transfer of electrical charge or signal transmission. Connecting conductors is a fundamental aspect of electrical circuits and systems, essential for completing circuits, establishing electrical pathways, and facilitating the transmission of electrical energy. [Diagram showing two conducting spheres, A and B, before contact at t=0. Sphere A has charge 2Q and radius 4R. Sphere B has charge Q and radius R. Their initial potentials are calculated.] V_initial(A) = k(2Q)/4R = kQ/2R V_initial(B) = kQ/R At time t = 0, when the conductors are not connected, the voltage at point B is lower than the [Diagram showing the two spheres connected by a wire. An arrow indicates the flow of charge from B to A.] When two conductors are connected or touched, an electric field is generated, flowing from the conductor of higher potential to the one of lower potential. Consequently, positive charge flows from the area of higher potential to the area of lower potential until the potentials of both conductors equalize. It's important to note that the charges on the two conductors may or may not be equal during this process. Thus, in this scenario, positive charge denoted as +q moves from conductor B to conductor A, resulting in an equalization of their potentials. Consequently, (V_A)_final = (V_B)_final k(2Q-q)/4R = k(Q+q)/R 2Q-q = 4(Q+q) 4Q-4q = 2Q + q 2Q = 5q q = 2Q/5 Hence, it follows that the final charge on conductor A, denoted as Q final (A), is equal to [Q - 2Q/5] = 3Q/5 Similarly, the final charge on conductor B, denoted as Q final (B), is calculated as [2Q + 2Q/5] = 12Q/5 This example underscores the observation that despite both conductors attaining equal potentials, their charges differ. Earthing of conductor Earthing of a conductor refers to the process of connecting the conductor to the Earth or a large conducting body, typically through a conducting wire or rod buried in the ground. This connection to the Earth serves several purposes, including providing a reference point for electrical systems, stabilizing voltage levels, and facilitating the dissipation of excess electrical charge. By grounding conductors, electrical hazards such as electric shocks, equipment damage, and electrical fires can be mitigated or prevented in electrical systems, ensuring the proper functioning and protection of equipment and individuals. When a conductor is connected to the Earth's surface, the potential of the Earth's surface is affected. For instance, if we place a positive charge +Q on the surface of the Earth, the electric potential on the Earth's surface is given by: V_E = kQ/R_E Considering that R_E ≈ 6400 km is significantly large, the expression for the Earth's potential simplifies to approximately zero: V_E≈0 Hence, the potential of the Earth can be approximated as zero. [Image of the Earth with a positive charge +Q on its surface.] When an isolated spherical conductor, initially possessing a charge Q and a radius R, is connected to the Earth, a positive charge +q transfers from the conductor to the Earth. Considering the Earth and conductor with a radius Re, both the conductor and the Earth reach an equilibrium where their potentials become equal. Therefore, [Image of a charged sphere with charge Q and radius R connected to the ground via an earthing symbol.] Earthing Symbol