The distance between charges 5 times 10^{-11} | vedclass

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

Question

(C) For a third charge $q$ to experience no net force,the forces exerted by the two charges $Q_1$ and $Q_2$ must be equal in magnitude and opposite in

Vedclass · Accepted Answer

$0.556$

Vedclass · Answer

(C) For a third charge $q$ to experience no net force,the forces exerted by the two charges $Q_1$ and $Q_2$ must be equal in magnitude and opposite in direction. Since the charges have opposite signs,the equilibrium point must lie outside the line segment joining them,closer to the charge with the smaller magnitude $(-2.7 	imes 10^{-11} \, C)$.Let the third charge $q$ be placed at a distance $x$ from the charge $Q_2 = -2.7 	imes 10^{-11} \, C$. The distance from $Q_1 = 5 	imes 10^{-11} \, C$ is $(x + 0.2) \, m$.Equating the magnitudes of the forces: $\frac{k |Q_1| |q|}{(x + 0.2)^2} = \frac{k |Q_2| |q|}{x^2}$.Substituting the values: $\frac{5 	imes 10^{-11}}{(x + 0.2)^2} = \frac{2.7 	imes 10^{-11}}{x^2}$.$\frac{5}{(x + 0.2)^2} = \frac{2.7}{x^2} \implies \frac{\sqrt{5}}{x + 0.2} = \frac{\sqrt{2.7}}{x}$.$2.236 x = 1.643 (x + 0.2) \implies 2.236 x = 1.643 x + 0.3286$.$0.593 x = 0.3286 \implies x \approx 0.554 \, m$. Given the options,the closest value is $0.556 \, m$.

The distance between charges $5 \times 10^{-11} \, C$ and $-2.7 \times 10^{-11} \, C$ is $0.2 \, m$. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is . . . . . . $m$.

Similar Questions

Select the correct statement from the following.

Three charges are placed at the vertices of an equilateral triangle of side '$a$' as shown in the figure. The force experienced by the charge placed at the vertex $A$ in a direction normal to $BC$ is

Two electric charges $+q$ and $+q$ are placed at a distance $r$. The force between them is $F$. If one charge is fixed and the other moves in a circle of radius $r$,the work done will be .......

Two charges are placed as shown in the figure. Where should a third charge be placed so that it remains at rest?

Two point charges of $+2\,\mu C$ and $+6\,\mu C$ repel each other with a force of $12\,N$. If each is given an additional charge of $-4\,\mu C$,then the force will become:

Vedclass Test Series

Exam Paper Generator

Online Exam Module