(C) For a uniformly charged thin spherical shell of radius $R$ and charge $q$,the electric potential at any point inside the shell (including the cent

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(C) For a uniformly charged thin spherical shell of radius $R$ and charge $q$,the electric potential at any point inside the shell (including the center) is constant and equal to the potential at the surface.The potential at any point $r \leq R$ is given by $V = \frac{1}{4 \pi \varepsilon_0} \frac{q}{R}$.Since point $C$ is at the center $(r = 0)$ and point $P$ is on the surface $(r = R)$,both points are at the same potential.Therefore,$V_C = V_P = \frac{1}{4 \pi \varepsilon_0} \frac{q}{R}$.The potential difference between points $C$ and $P$ is $V_C - V_P = 0$.

Class 12 Physics Electric Potential and Capacitance Electric potential

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$A$ thin spherical shell is charged by some source. The potential difference between the two points $C$ (the center) and $P$ (a point on the surface) as shown in the figure is: (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}$)

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$1 \times 10^5 \text{ V}$
B
$0.5 \times 10^5 \text{ V}$
C
Zero
D
$3 \times 10^5 \text{ V}$

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Electric Potential and Capacitance

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$A$ thin spherical shell is charged by some source. The potential difference between the two points $C$ (the center) and $P$ (a point on the surface) as shown in the figure is: (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}$)

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$A$ uniformly charged ring of radius $3a$ and total charge $q$ is placed in the $xy$-plane centered at the origin. $A$ point charge $q$ is moving towards the ring along the $z$-axis and has speed $v$ at $z = 4a$. The minimum value of $v$ such that it crosses the origin is

$A$ charge of $8 \; mC$ is located at the origin. Calculate the work done in $J$ in taking a small charge of $-2 \times 10^{-9} \; C$ from a point $P (0, 0, 3 \; cm)$ to a point $Q (0, 4 \; cm, 0)$,via a point $R (0, 6 \; cm, 9 \; cm)$.

$A$ proton is $1840$ times heavier than an electron. When it is accelerated through a potential difference of $1 \ kV$,its kinetic energy is .......... $keV$.

An infinite number of charges, each numerically equal to $q$ and of the same sign, are placed along the $x-$axis at $x = 1, 2, 4, 8, \dots \, \text{meters}$. The electric potential at $x = 0$ due to this set of charges is:

Three charges each of value $+q$ are placed at the corners of an isosceles triangle $ABC$ with sides $AB = AC = 2a$. The midpoints of $AB$ and $AC$ are $D$ and $E$ respectively. The work done in taking a charge $Q$ from $D$ to $E$ is (where $\varepsilon_0$ is the permittivity of free space):

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