(A) The work done in bringing a charge $q_0$ from infinity to a point is given by $W = q_0 V$,where $V$ is the electric potential at that point due to

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(A) The work done in bringing a charge $q_0$ from infinity to a point is given by $W = q_0 V$,where $V$ is the electric potential at that point due to the existing charges.In a regular hexagon of side $d$,the distance of each corner from the centre is $d$.The electric potential $V$ at the centre due to the six charges is the sum of the potentials due to each individual charge:$V = \frac{1}{4 \pi \varepsilon_0} \left( \frac{+q}{d} + \frac{-q}{d} + \frac{+q}{d} + \frac{-q}{d} + \frac{+q}{d} + \frac{-q}{d} \right)$$V = \frac{1}{4 \pi \varepsilon_0 d} (q - q + q - q + q - q)$$V = 0$Therefore,the work done $W = q_0 \times 0 = 0$.

Class 12 Physics Electric Potential and Capacitance Electric potential

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Six charges $+q, -q, +q, -q, +q$ and $-q$ are fixed at the corners of a hexagon of side $d$ as shown in the figure. The work done in bringing a charge $q_0$ to the centre of the hexagon from infinity is: ($\varepsilon_0$ = permittivity of free space)

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A
$0$
B
$\frac{-q^2}{4 \pi \varepsilon_0 d}$
C
$\frac{-q^2}{4 \pi \varepsilon_0 d} \left(3-\frac{1}{\sqrt{2}}\right)$
D
$\frac{-q^2}{4 \pi \varepsilon_0 d} \left(6-\frac{1}{\sqrt{2}}\right)$

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Electric Potential and Capacitance

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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 $cm$)?

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Two electric charges of $9 \mu C$ and $-3 \mu C$ are placed $0.16 \ m$ apart in air. There will be a point $P$ on the line joining the two charges and between them where the electric potential is zero. The distance of $P$ from the $9 \mu C$ charge is: (in $m$)

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Six charges $+q, -q, +q, -q, +q$ and $-q$ are fixed at the corners of a hexagon of side $d$ as shown in the figure. The work done in bringing a charge $q_0$ to the centre of the hexagon from infinity is: ($\varepsilon_0$ = permittivity of free space)

Similar Questions

Two conducting hollow spheres of radii $R$ and $3R$ are found to have $Q$ charge on their outer surfaces when both are connected with a long wire. $A$ charge $q'$ is kept at the centre of the bigger sphere. Which of the following is true?

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

Consider three concentric metal shells $A$,$B$,and $C$ with radii $a$,$b$,and $c$ respectively,as shown in the figure $(a < b < c)$. Their surface charge densities are $\sigma$,$-\sigma$,and $\sigma$ respectively. Calculate the electric potential on the surface of shell $A$.

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 $cm$)?

Two electric charges of $9 \mu C$ and $-3 \mu C$ are placed $0.16 \ m$ apart in air. There will be a point $P$ on the line joining the two charges and between them where the electric potential is zero. The distance of $P$ from the $9 \mu C$ charge is: (in $m$)

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