(C) The electric potential $V$ at a distance $r$ from a point charge $Q$ is given by $V = \frac{kQ}{r}$.The distance of point $P(\sqrt{3}, \sqrt{3})$

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(C) The electric potential $V$ at a distance $r$ from a point charge $Q$ is given by $V = \frac{kQ}{r}$.The distance of point $P(\sqrt{3}, \sqrt{3})$ from the origin $(0,0)$ is $r_1 = \sqrt{(\sqrt{3})^2 + (\sqrt{3})^2} = \sqrt{3 + 3} = \sqrt{6} \text{ m}$.The distance of point $Q(\sqrt{6}, 0)$ from the origin $(0,0)$ is $r_2 = \sqrt{(\sqrt{6})^2 + 0^2} = \sqrt{6} \text{ m}$.Since $r_1 = r_2 = \sqrt{6} \text{ m}$,the potential at point $P$ is $V_P = \frac{kQ}{r_1}$ and the potential at point $Q$ is $V_Q = \frac{kQ}{r_2}$.Therefore,the potential difference $V_P - V_Q = \frac{kQ}{r_1} - \frac{kQ}{r_2} = 0 \text{ V}$.

Class 12 Physics Electric Potential and Capacitance Electric potential

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An electric charge $10^{-6} \mu C$ is placed at the origin $(0,0) \text{ m}$ of an $X-Y$ coordinate system. Two points $P$ and $Q$ are situated at $(\sqrt{3}, \sqrt{3}) \text{ m}$ and $(\sqrt{6}, 0) \text{ m}$ respectively. The potential difference between the points $P$ and $Q$ will be:

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A
$\sqrt{3} \text{ V}$
B
$\sqrt{6} \text{ V}$
C
$0 \text{ V}$
D
$3 \text{ V}$

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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:

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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

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Two charges $5 \times 10^{-8} \; C$ and $-3 \times 10^{-8} \; C$ are located $16 \; cm$ apart. At what point$(s)$ on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

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An electric charge $10^{-6} \mu C$ is placed at the origin $(0,0) \text{ m}$ of an $X-Y$ coordinate system. Two points $P$ and $Q$ are situated at $(\sqrt{3}, \sqrt{3}) \text{ m}$ and $(\sqrt{6}, 0) \text{ m}$ respectively. The potential difference between the points $P$ and $Q$ will be:

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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:

The mass of a particle is $400$ times that of an electron and its charge is double that of an electron. The particle is accelerated by a potential difference of $5 \; V$. If the particle was initially at rest,what will be its final kinetic energy in $eV$?

Two conducting spheres of radii $9 \,cm$ and $1 \,cm$ are separated by a distance of $20 \,cm$ in free space. If the spheres are charged to the same potential of $10 \,V$ each, the force of repulsion between them is

$A$ 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

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