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 at points $A$ and $B$,separated by a distance $x$. The charge $q$ is placed at point $C$,the midpoint of $AB$,so $AC =

Vedclass · Accepted Answer

$ - \frac{Q}{4} $

Vedclass · Answer

(B) Let the two charges $Q$ be at points $A$ and $B$,separated by a distance $x$. The charge $q$ is placed at point $C$,the midpoint of $AB$,so $AC = CB = x/2$.For the system to be in equilibrium,the net force on each charge must be zero.Consider the equilibrium of charge $Q$ at point $A$. The force exerted by charge $Q$ at $B$ on $A$ is $F_{BA} = \frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{x^2}$ (repulsive).The force exerted by charge $q$ at $C$ on $A$ is $F_{CA} = \frac{1}{4 \pi \varepsilon_0} \frac{qQ}{(x/2)^2}$ (attractive,so $q$ must be negative).For equilibrium,$F_{BA} + F_{CA} = 0$,so $\frac{1}{4 \pi \varepsilon_0} \frac{Q^2}{x^2} + \frac{1}{4 \pi \varepsilon_0} \frac{qQ}{x^2/4} = 0$.$\frac{Q^2}{x^2} + \frac{4qQ}{x^2} = 0 \Rightarrow Q + 4q = 0 \Rightarrow q = -\frac{Q}{4}$.

$A$ 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

For a suitably chosen real constant $a$,let a function $f: R - \{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f\left(\frac{-1}{2}\right)$ is equal to

$A$ body weighs $700 \, gm \, wt$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth?

Two identical particles are moving with same velocity $v$ as shown in the figure. If the collision is completely inelastic,then:

The basic unit of classification for plants and animals is ....

The function $f(x) = x e^{-x}, \forall x \in R$ attains a maximum value at $x$ equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module