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) The charges are $q_A = q/3$,$q_B = q/3$,and $q_C = -2q/3$. In $	riangle ABC$,since $A, B, C$ are on a circle with center $O$,$OA = OB = OC = R$.

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) The charges are $q_A = q/3$,$q_B = q/3$,and $q_C = -2q/3$. In $	riangle ABC$,since $A, B, C$ are on a circle with center $O$,$OA = OB = OC = R$. Given $\angle CAB = 60^{\circ}$,in $	riangle OAC$,$OA = OC = R$,so $\angle OCA = \angle OAC = 60^{\circ}$,implying $	riangle OAC$ is equilateral. Thus,$AC = R$. Similarly,for $	riangle OBC$,since $\angle ACB = 90^{\circ}$ (angle in a semicircle if $AB$ is diameter,but here $AB$ is a chord),we calculate the distance $BC$. Using the law of cosines in $	riangle OBC$,or geometry: $BC = \sqrt{R^2 + R^2 - 2R^2 \cos(120^{\circ})} = R\sqrt{3}$. The force between $C$ and $B$ is $F_{BC} = \frac{1}{4 \pi \varepsilon_0} \frac{|q_C| |q_B|}{(BC)^2} = \frac{1}{4 \pi \varepsilon_0} \frac{(2q/3)(q/3)}{(R\sqrt{3})^2} = \frac{1}{4 \pi \varepsilon_0} \frac{2q^2/9}{3R^2} = \frac{q^2}{54 \pi \varepsilon_0 R^2}$. 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

Which of the following physical quantities have the same dimensions?

$A$ uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

Which of the field patterns given below is valid for electric field as well as for magnetic field?

Charges are placed on the vertices of a square as shown. Let $\vec E$ be the electric field and $V$ be the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively,then

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting, which of the following statements is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module