Question

Three charges are placed at points A, B and P The magnitude of these three charges are $q_1,q_2$ and -q Resultant force on the charge at P due to others :

• A. will pass through the centre of AB if $\frac{q_1}{q_2}=\frac{P{A}^3}{P{B}^3}$
• B. will pass through the centre of AB if $\frac{q_1}{q_2}=\frac{P{A}^2}{P{B}^2}$
• C. will pass through the centre of AB if PA = PB and $q_1=q_2$
• D. will pass through the centre of AB if PA = PB for all values of $q_{1}and{q}_2$

Answer 1

Answer: (A), (C)

The correct options are
A will pass through the centre of AB if $\frac{q_1}{q_2}=\frac{P{A}^3}{P{B}^3}$
C will pass through the centre of AB if PA = PB and $q_1=q_2$

Resultant Force to pass through the center,

$F_{q_1}=k.q_{1}q/P{A}^2$ in the direction of PA

$F_{q_2}=k.q_{2}q/P{B}^2$ in the direction of PB

$\overrightarrow{F}=\overrightarrow{F_1}+\overrightarrow{F_2}$

$F=F_1+F_2+2F_1{F}_2\cos \theta$

Now force to pass throgh center. The vector components of force in direction perpendicular to PM must be cancel each other.

Therefore, Therefore, to satisfy this from properties of triangle

We get $F_1/F_2=PA/PB$

This gives $q_1/q_2=P{A}^3/P{B}^3$

and this satisfies when q_1=q_2 and PA=PB

Therefore, option (A) and option (C)