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 =

• A. -q
• B. -2q
• C. $-\frac{q}{2}$
• D. 4q

Answer 1

The correct option is (A) -q

Step 1, Given data

Charges are 4q, Q and q

Placed on a straight line such that Q is in the middle of the 4q and q

Step 2, Find the value of Q such that force on q is zero

We can write

The force between 4q and q; $F_1=\frac{1}{4\pi {ϵ}_0}.\frac{4q\times q}{l^2}$

And,
The force between Q and q; $F_2=\frac{1}{4\pi {ϵ}_0}.\frac{Q\times q}{(\frac{l}{2}{)}^2}$

Now according to the question the net force is zero

So,
$F_1+F_2=0$ or $\frac{4q^2}{l^2}=-\frac{4Qq}{l^2}\Rightarrow Q=-q$

Hence the value of Q will be -q.