Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown in the figure. Three charges are $+Q$ and three are $-Q$ arranged alternately. The electric field intensity at a point on the line passing through the centre $O$ and perpendicular to the plane of the figure at a large distance $x (x \gg a)$ from $O$ is (Let $\frac{1}{4 \pi \epsilon_0} = k$):

  • A
    $k \times \frac{4 Q a}{x^3}$
  • B
    $k \times \frac{2 Q a}{x^3}$
  • C
    $k \times \frac{8 Q a}{x^3}$
  • D
    $0$

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Consider the following statements about electric field intensity and electric potential.
$A$. The electric field intensity due to a charged spherical shell is inversely proportional to the square of its distance from the center for points outside the shell.
$B$. The electric potential due to a point charge is inversely proportional to the distance between the charge and the point.

Five point charges each having magnitude $q$ are placed at the corners of a regular hexagon as shown in the figure. The net electric field at the centre $O$ is $\vec E$. To make the net electric field at $O$ equal to $6\vec E$,the charge placed on the remaining sixth corner should be: (in $,q$)

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What will be the magnitude of the electric field at point $O$ as shown in the figure? Each side of the figure has length $l$ and segments are perpendicular to each other.

$A$ spherical conductor of radius $2 \text{ cm}$ is uniformly charged with $3 \text{ nC}$. What is the electric field at a distance of $3 \text{ cm}$ from the center of the sphere?

Obtain the equation of electric field at a point due to a system of $n$ point charges.

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