A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the

step 1 Hi everyone there is a thin spherical cell of radius r having the charge Q another charge Q is p

A thin spherical conducting shell of radius R has a charge...

A thin spherical conducting shell of radius $\mathrm{R}$ has a charge q. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point p a distance $(\mathrm{R} / 2)$ from the centre of the shell is ..... (A) $\left[(q+Q) /\left(4 \pi \epsilon_{0}\right)\right](2 / R)$ (B) $\left[\left\{(2 Q) /\left(4 \pi \epsilon_{0} R\right)\right\}-\left\{(2 Q) /\left(4 \pi \epsilon_{0} R\right)\right]\right.$ (C) $\left[\left\{(2 Q) /\left(4 \pi \in_{0} R\right)\right\}+\left\{q /\left(4 \pi \epsilon_{0} R\right)\right]\right.$ (D) $\left[(2 \mathrm{Q}) /\left(4 \pi \epsilon_{0} \mathrm{R}\right)\right]$

A thin spherical conducting shell of radius $\mathrm{R}$ has a charge q. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point p a distance $(\mathrm{R} / 2)$ from the centre of the shell is .....
(A) $\left[(q+Q) /\left(4 \pi \epsilon_{0}\right)\right](2 / R)$
(B) $\left[\left\{(2 Q) /\left(4 \pi \epsilon_{0} R\right)\right\}-\left\{(2 Q) /\left(4 \pi \epsilon_{0} R\right)\right]\right.$
(C) $\left[\left\{(2 Q) /\left(4 \pi \in_{0} R\right)\right\}+\left\{q /\left(4 \pi \epsilon_{0} R\right)\right]\right.$
(D) $\left[(2 \mathrm{Q}) /\left(4 \pi \epsilon_{0} \mathrm{R}\right)\right]$

Key Concepts

Electrostatic Potential

Electrostatic potential is the work done per unit charge in bringing a test charge from infinity to a given point in an electric field. This concept is fundamental because it allows the determination of voltage at any point in space due to different charge distributions, and it is additive so that contributions from multiple charges can be summed to obtain a net potential.

Superposition Principle

The superposition principle in electrostatics states that the total electric potential at a point produced by several charges is the algebraic sum of the potentials due to each individual charge. This principle is crucial when dealing with multiple charge configurations because it simplifies the analysis of complex electrostatic problems by allowing independent consideration of each charge's effect.

Properties of Conductors in Electrostatic Equilibrium

In electrostatics, conductors have the property that the electric field within their material is zero when in equilibrium, and excess charges reside on their surfaces. Consequently, the potential inside a conductor is constant. This concept is essential when analyzing problems involving conducting shells or bodies, as it helps determine the electric potential distribution both inside and outside the conductive material.

Spherical Symmetry in Electrostatics

Spherical symmetry greatly simplifies the analysis of electrostatic problems because the potential and electric field depend only on the radial distance from the center of the sphere. This symmetry allows for the use of Gauss’s law to derive expressions for electric fields and potentials in and around spherical charge distributions, making it an important concept when dealing with spherical configurations.

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