Three charges Q, +q and +q are placed at the | vedclass

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

Question

(B) The electrostatic potential energy $(U)$ of a system of point charges is given by the sum of the potential energies of all pairs of charges: $U =

Vedclass · Accepted Answer

$\frac{-2q}{2 + \sqrt{2}}$

Vedclass · Answer

(B) The electrostatic potential energy $(U)$ of a system of point charges is given by the sum of the potential energies of all pairs of charges: $U = \sum \frac{k q_i q_j}{r_{ij}}$.For the given system,the charges are $Q, +q, +q$ at the vertices of a right-angled isosceles triangle with sides $a, a$ and hypotenuse $\sqrt{2}a$.The pairs are $(Q, q)$ at distance $a$,$(Q, q)$ at distance $a$,and $(q, q)$ at distance $\sqrt{2}a$.Setting the total potential energy to zero:$U = \frac{kQq}{a} + \frac{kQq}{a} + \frac{kq^2}{\sqrt{2}a} = 0$$\frac{k}{a} [2Qq + \frac{q^2}{\sqrt{2}}] = 0$$2Qq = -\frac{q^2}{\sqrt{2}}$$Q = -\frac{q}{2\sqrt{2}} = -\frac{q\sqrt{2}}{4}$Alternatively,simplifying the expression from the options:$Q = -\frac{q}{2(1 + 1/\sqrt{2})} = -\frac{q}{2 + \sqrt{2}}$.Thus,the correct option is $B$.

Three charges $Q, +q$ and $+q$ are placed at the vertices of a right-angled isosceles triangle as shown in the figure. The net electrostatic potential energy of the system is zero. Then $Q$ is equal to:

Similar Questions

Three point charges $3 \text{ nC}$,$6 \text{ nC}$,and $9 \text{ nC}$ are placed at the corners of an equilateral triangle of side $0.1 \text{ m}$. The potential energy of the system is:

The charges $+q$,$+q$,and $Q$ are placed at the vertices of an equilateral triangle of side $a$. If the net electrostatic potential energy of the system is zero,then $Q$ is equal to:

The condition for minimum potential energy of an electric dipole in a uniform electric field is ......

$A$ system of two charges separated by a certain distance apart stores electrical potential energy. If the distance between them is increased,the potential energy of the system,

Vedclass Test Series

Exam Paper Generator

Online Exam Module