Three charges 4q, Q and q are in a straight line in the position of 0, l 2 and l respectively. The resultant force on q will be zero, if Q = Options: A . &nbsp-q B . &nbsp-2q C . &nbsp−q2 D . &nbsp4q E . &nbspIf assertion is false but reason is true.

Answer: Option A : A The force between 4qand q; F 1 = 1 4 π ϵ 0 . 4 q × q l 2 The force between Qand q; F 2 = 1 4 π ϵ 0 . Q × q ( l 2 ) 2 We want F 1 + F 2 = 0 or 4 q 2 l 2 = − 4 Q q l 2 ⇒ Q = − q

Three charges 4q, Q and q are in a straight line in the position of 0,l2 and l r

Question

Three charges 4q, Q and q are in a straight line in the position of 0,

\frac{l}{2}

and l respectively. The resultant force on q will be zero, if Q =

Answer: Option A
:
A
The force between 4qand q;

F_{1} = \frac{1}{4 π ϵ_{0}} . \frac{4 q \times q}{l^{2}}

The force between Qand q;

F_{2} = \frac{1}{4 π ϵ_{0}} . \frac{Q \times q}{(\frac{l}{2})^{2}}

We want

F_{1} + F_{2} = 0

\frac{4 q^{2}}{l^{2}} = - \frac{4 Q q}{l^{2}} \Rightarrow Q = - q

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