A charge q is placed at the centre of the lin | vedclass

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

Question

(B) Let the two charges $Q$ be placed at points $A$ and $B$ separated by a distance $2r$. The charge $q$ is placed at the midpoint $O$.For the system

Vedclass · Accepted Answer

$-\frac{Q}{4}$

Vedclass · Answer

(B) Let the two charges $Q$ be placed at points $A$ and $B$ separated by a distance $2r$. The charge $q$ is placed at the midpoint $O$.For the system to be in equilibrium,the net force on each charge must be zero.Consider the force on charge $Q$ at point $A$:The force due to charge $q$ at $O$ is $F_1 = \frac{1}{4 \pi \varepsilon_0} \frac{Qq}{r^2}$ (attractive,towards $O$).The force due to charge $Q$ at $B$ is $F_2 = \frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{(2r)^2} = \frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{4r^2}$ (repulsive,away from $B$).For equilibrium,$F_1 + F_2 = 0$,so $\frac{1}{4 \pi \varepsilon_0} \frac{Qq}{r^2} + \frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{4r^2} = 0$.Solving for $q$: $\frac{Qq}{r^2} = -\frac{Q^2}{4r^2} \Rightarrow q = -\frac{Q}{4}$.

Column $I$	Column $II$
$(a)$ Proliferative Phase	$(i)$ Breakdown of endometrium
$(b)$ Secretory Phase	$(ii)$ Follicular phase
$(c)$ Menstruation	$(iii)$ Luteal Phase

$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

Similar Questions

The coordination number of a metal crystallizing in a hexagonal close-packed structure is

Statement $P$: Every living organism exhibits unique characteristics such as reproduction,growth,development,adaptation,and death.
Statement $Q$: Energy transformation is essential for every living organism.

Match the items given in Column $I$ with those in Column $II$ and select the correct option given below:

Column $I$ Column $II$

$(a)$ Proliferative Phase $(i)$ Breakdown of endometrium

$(b)$ Secretory Phase $(ii)$ Follicular phase

$(c)$ Menstruation $(iii)$ Luteal Phase

The incentre of the triangle with vertices $A(1, \sqrt{3})$,$B(0,0)$,and $C(2,0)$ is

$A$ ball is projected from the ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path,it makes an elastic collision with a vertical wall and returns to the ground. The total time of flight of the ball is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module