Consider a system of three charges frac{q}{3} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given charges are $q_A = \frac{q}{3}$,$q_B = \frac{q}{3}$,and $q_C = \frac{-2q}{3}$.In $	riangle ABC$,since $A, B, C$ lie on a circle of radius $

Vedclass · Accepted Answer

The magnitude of the force between the charges at $C$ and $B$ is $\frac{q^2}{54\pi \varepsilon_0 R^2}$.

Vedclass · Answer

(C) Given charges are $q_A = \frac{q}{3}$,$q_B = \frac{q}{3}$,and $q_C = \frac{-2q}{3}$.In $	riangle ABC$,since $A, B, C$ lie on a circle of radius $R$ and $\angle CAB = 60^{\circ}$,the chord $BC$ subtends an angle at the circumference. The distance $BC$ can be calculated using the law of sines or geometry. Since $O$ is the center,$\angle COB = 2 \angle CAB = 120^{\circ}$.The distance $BC = 2R \sin(60^{\circ}) = 2R \frac{\sqrt{3}}{2} = R\sqrt{3}$.The magnitude of the electrostatic force between charges at $C$ and $B$ is given by Coulomb's Law:$F = \frac{1}{4\pi \varepsilon_0} \frac{|q_C \cdot q_B|}{(BC)^2} = \frac{1}{4\pi \varepsilon_0} \frac{|(\frac{-2q}{3}) \cdot (\frac{q}{3})|}{(R\sqrt{3})^2}$$F = \frac{1}{4\pi \varepsilon_0} \frac{2q^2/9}{3R^2} = \frac{2q^2}{108\pi \varepsilon_0 R^2} = \frac{q^2}{54\pi \varepsilon_0 R^2}$.Thus,option $C$ is correct.

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $\frac{-2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

Similar Questions

'Amoebiasis' (amoebic dysentery) is caused by

If a solid sphere of mass $1 \ kg$ and radius $0.1 \ m$ rolls without slipping at a uniform velocity of $1 \ m/s$ along a straight line on a horizontal floor,the kinetic energy is

The ratio $\frac{K_p}{K_c}$ for the reaction $CO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons CO_{2(g)}$ is

If $f: R \rightarrow R$ is defined by $f(x) = \frac{1}{2 - \cos 3x}$ for each $x \in R$,then the range of $f$ is

Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?

Vedclass Test Series

Exam Paper Generator

Online Exam Module