A thin spherical conducting shell of radius R | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The potential at point $P$ inside the shell is the sum of the potential due to the charge $Q$ at the center and the potential due to the charge $q

Vedclass · Accepted Answer

$\frac{2Q}{4 \pi \varepsilon_0 R} + \frac{q}{4 \pi \varepsilon_0 R}$

Vedclass · Answer

(D) The potential at point $P$ inside the shell is the sum of the potential due to the charge $Q$ at the center and the potential due to the charge $q$ on the shell.For a point inside a conducting shell,the potential due to the shell's charge $q$ is constant and equal to the potential at its surface,which is $V_{shell} = \frac{kq}{R}$.The potential due to the point charge $Q$ at distance $r = R/2$ is $V_{point} = \frac{kQ}{R/2} = \frac{2kQ}{R}$.Therefore,the total potential at point $P$ is $V_P = V_{point} + V_{shell} = \frac{2kQ}{R} + \frac{kq}{R}$.Substituting $k = \frac{1}{4 \pi \varepsilon_0}$,we get $V_P = \frac{2Q}{4 \pi \varepsilon_0 R} + \frac{q}{4 \pi \varepsilon_0 R}$.

$A$ thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is:

Similar Questions

The electric potential at a point at a distance $x$ from the center inside a conducting sphere of radius $R$ charged with charge $Q$ is:

An electron (charge = $1.6 \times 10^{-19} \text{ C}$) is accelerated through a potential of $100,000 \text{ V}$. The energy acquired by the electron is:

Two point charges $q_1 = 4 \times 10^{-8} \ C$ and $q_2 = -6 \times 10^{-8} \ C$ are placed at points $A$ and $B$ respectively,which are $50 \ cm$ apart. At what distance from point $A$ on the line $AB$ is the electric potential zero (in $cm$)?

Three concentric spherical shells have radii $a, b$ and $c$ $(a < b < c)$ and have surface charge densities $\sigma, -\sigma$ and $\sigma$ respectively. If $V_A, V_B$ and $V_C$ denote the potentials of the three shells,then,for $c = a + b$,we have

An electric charge $10^{-3} \, \mu C$ is placed at the origin $(0, 0)$ of an $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be $V$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module