Three charge q, Q and 4q are placed in a straight line of length l at points distant 0, (1)/(2) and l respectively from one end. In order to make the net froce on q zero, the charge Q must be equal to

Correct answer: A. -q (F_ net )_ q =0 k Qq (( )/(2))^ 2 +k 4 q^ 2 ^ 2 =0 array l where k= 1 4 π _ 0 4 Qq+4 q^ 2 =0 Q=-q array

BITSAT 2020

BITSAT 2020 · Physics · Electrostatics

Three charge q, Q and 4q are placed in a straight line of length l...

Three charge q, Q and 4q are placed in a straight line of length

l

at points distant

0, \frac{1}{2}

and

l

respectively from one end. In order to make the net froce on q zero, the charge Q must be equal to

A. $-\mathrm{q}$

\left(\mathrm{F}_{\text{net }}\right)_{\mathrm{q}}=0\Rightarrow \quad \mathrm{k} \frac{\mathrm{Qq}}{\left(\frac{\ell}{2}\right)^{2}}+\mathrm{k} \frac{4 \mathrm{q}^{2}}{\ell^{2}}=0

\begin{array}{l} \text{ where } \mathrm{k}=\frac{1}{4 \pi \varepsilon_{0}} \\ \Rightarrow 4 \mathrm{Qq}+4 \mathrm{q}^{2}=0 \quad \Rightarrow \mathrm{Q}=-\mathrm{q} \end{array}