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

In which of the following are vessels and companion cells found?

$A$ battery is used to charge a parallel plate capacitor until the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor to the work done by the battery is

In how many ways can $8$ identical balls be distributed into $3$ distinct boxes such that no box remains empty?

In which of the following reactions,$H_2O_2$ acts as a reducing reagent?

The figure shows the vertical section of a frictionless surface. $A$ block of mass $2\, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is ................ $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module