5 charges each of magnitude 10^{-5} ,C and mass 1 ,kg are placed (fixed) symmetrically about a movab

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1. Electric Charges and Fields

hard

$5$ charges each of magnitude $10^{-5} \,C$ and mass $1 \,kg$ are placed (fixed) symmetrically about a movable central charge of magnitude $5 \times 10^{-5} \,C$ and mass $0.5 \,kg$ as shown in the figure given below. The charge at $P_1$ is removed. The acceleration of the central charge is [Given, $\left.O P_1=O P_2=O P_3=O P_4=O P_5=1 m , \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right]$

$9 \,ms ^{-2}$ upwards

$9 \,ms ^{-2}$ downwards

$4.5 \,ms ^{-2}$ upwards

$4.5 \,ms ^{-2}$ downwards

(KVPY-2009)

Solution

(c)

Forces on charge at point $O$ initially balances each other as it is given that acceleration occurs when charge at point $P_1$ is removed. This means resultant of force due to charges at points $P_2, P_3, P_4$ and $P_5$ is equal and opposite to force due to at point $P_1$.

Hence, acceleration of charge at point $O$ is directed along $O P_1$.

Acceleration $=\frac{F}{m}$

$=\frac{(\frac{K q_1 q_2}{r^2})}{m}$

$=\frac{9 \times 10^9 \times 10^{-5} \times 5 \times 10^{-5}}{(1)^2 \times 1}$

$=4.5 \,ms ^{-2}$

Standard 12

Physics

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r$. The coulomb force $\overrightarrow F $ between the two is (Where $K = \frac{1}{{4\pi {\varepsilon _0}}}$)

medium

(AIPMT-2003)

Two charges placed in air repel each other by a force of ${10^{ – 4}}\,N$. When oil is introduced between the charges, the force becomes $2.5 \times {10^{ – 5}}\,N$. The dielectric constant of oil is

easy

Assertion : A deuteron and an $\alpha -$ particle are placed in an electric field. If $F_1$ and $F_2$ be the forces acting on them and $a_1$ and $a_2$ be their accelerations respectively then, $a_1 = a_2$.

Reason : Forces will be same in electric field

medium

(AIIMS-2015)

Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.

hard

(JEE MAIN-2022)

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

medium

Solution

Similar Questions

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r$. The coulomb force $\overrightarrow F $ between the two is (Where $K = \frac{1}{{4\pi {\varepsilon _0}}}$)

Two charges placed in air repel each other by a force of ${10^{ – 4}}\,N$. When oil is introduced between the charges, the force becomes $2.5 \times {10^{ – 5}}\,N$. The dielectric constant of oil is

Assertion : A deuteron and an $\alpha -$ particle are placed in an electric field. If $F_1$ and $F_2$ be the forces acting on them and $a_1$ and $a_2$ be their accelerations respectively then, $a_1 = a_2$. Reason : Forces will be same in electric field

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Assertion : A deuteron and an $\alpha -$ particle are placed in an electric field. If $F_1$ and $F_2$ be the forces acting on them and $a_1$ and $a_2$ be their accelerations respectively then, $a_1 = a_2$.

Reason : Forces will be same in electric field