12 positive charges of magnitude q are placed on a circle of radius R in a manner that they are equa

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1. Electric Charges and Fields

medium

$12$ positive charges of magnitude $q$ are placed on a circle of radius $R$ in a manner that they are equally spaced. A charge $Q$ is placed at the centre, if one of the charges $q$ is removed, then the force on $Q$ is

zero

$\frac{q Q}{4 \pi \varepsilon_0 R^2}$ away from the position of the removed charge

$\frac{11 q Q}{4 \pi \varepsilon_0 R^2}$ away from the position of the removed charge

$\frac{q Q}{4 \pi \varepsilon_0 R^2}$ towards the position of the removed charge

(KVPY-2010)

Solution

(d)

Force on charge $Q$ is initially zero as forces of $12$ charges balances each other.

As shown in above figure, forces of diametrically opposite charges balances each other, hence net force on $Q$ is zero. When one of the charge $q\left(\right.$ let $\left.q_1\right)$ is removed, net force on $Q$ is now the unbalanced force of diametrically opposite charge.

i.e. Force, $F=\frac{k q Q}{R^2}=\frac{q Q}{4 \pi \varepsilon_0 R^2}$ and this force vector points towards the position of the removed charge.

Standard 12

Physics

Force between $A$ and $B$ is $F$. If $75\%$ charge of $A$ is transferred to $B$ then force between $A$ and $B$ is

medium

Three equal charges $+q$ are placed at the three vertices of an equilateral triangle centred at the origin. They are held in equilibrium by a restoring force of magnitude $F(r)=k r$ directed towards the origin, where $k$ is a constant. What is the distance of the three charges from the origin?

hard

(KVPY-2010)

Six charges are placed at the corner of a regular hexagon as shown. If an electron is placed at its centre $O$, force on it will be:

normal

Two copper balls, each weighing $10\,g$ are kept in air $10\, cm$ apart. If one electron from every ${10^6}$ atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is $63.5$)

medium

Two charges $\mathrm{q}$ and $-3\mathrm{q}$ are placed fixed on $x-$ axis separated by distance $\mathrm{'d'}$. Where should a third charge $2\mathrm{q}$ be placed such that it will not experience any force ?

medium

$12$ positive charges of magnitude $q$ are placed on a circle of radius $R$ in a manner that they are equally spaced. A charge $Q$ is placed at the centre, if one of the charges $q$ is removed, then the force on $Q$ is

Solution

Similar Questions

Force between $A$ and $B$ is $F$. If $75\%$ charge of $A$ is transferred to $B$ then force between $A$ and $B$ is

Three equal charges $+q$ are placed at the three vertices of an equilateral triangle centred at the origin. They are held in equilibrium by a restoring force of magnitude $F(r)=k r$ directed towards the origin, where $k$ is a constant. What is the distance of the three charges from the origin?

Six charges are placed at the corner of a regular hexagon as shown. If an electron is placed at its centre $O$, force on it will be:

Two copper balls, each weighing $10\,g$ are kept in air $10\, cm$ apart. If one electron from every ${10^6}$ atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is $63.5$)

Two charges $\mathrm{q}$ and $-3\mathrm{q}$ are placed fixed on $x-$ axis separated by distance $\mathrm{'d'}$. Where should a third charge $2\mathrm{q}$ be placed such that it will not experience any force ?

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