Test: Forces between Multiple Charges (NCERT) - NEET MCQ

Let a charge 2q be placed at P, at a distance l from A where charge q is placed, as shown in figure.
The charge 2q will not experience any force, when  force of repulsion on it due to q is balanced by force of attraction on it due to -3q at B where AB = d
or 
(l + d)² = 3l² or 2l² - 2ld - d² = 0

If charge 2q is placed between A and B then 

From diagram, force on q₁(= q) at A,


where  is the unit vector along BC 
Force on 
(where   is the unit vector along AC)
Force on q₃(= -q) at C,

where  unit vector along the direction bisecting ∠BCA

For the system to be in equilibrium, net force on q = 0 or 
or Q = (-q)/4 or Q/q = -(1/4)

Forces of repulsion on 1μC charge at O due to 3 μC charge, at A and C are equal and opposite. So they cancel each other.
Similarly, forces of attraction of 1μC charge at O due to -4μC charges at B and D are also equal and opposite. So they also cancel each other.
Hence the net force on the charge of 1μC at O is zero. 

 As shown in figured raw AD ⊥ BC.



Distance AO of the centroid O from A

∴ Force on Q at O due to charge q₁ = q at A,

Similarly, force on O due to charge q₂ = q at B
 along BO and force on Q due to charge q₃ = q at c

Angle between forces F₂ and F₃ = 120°
By parallelogram law, resultant of  along OA
∴ Total force on Q =