Question

Three point-charges q1, q2, q3 are in line at equal
distances. q2 and q3 are opposite in sign. Find the
magnitude and sign of q1, if the net force on q3is zero.
​

Answer 1

It could be - or+

Let

Q1 x

Q2+

Q3-

But q3 0

So remaing is q2. + or x could be positive or negative

Answer 2

Answer:

The charge of q₁ has the magnitude four times of charge q₂ and sign as that of q₃

Explanation:

Given that,

Three point-charges q₁, q₂, q₃ are in line at equal  distances. q₂ and q₃ are opposite in sign.

Let q₁ be the test charge.

The charges of q₂ and q₃ are opposite in sign there exists an attractive force between them.

If the net force on q₃ is zero.

So, The force between q₁ and q₃ must be force of repulsion.

Now, The force on q₃ due to q₁

$F = \dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q_{1}q_{3}}{(2r)^2}$

The force on q₃ due to q₂

$F' = -\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q_{2}q_{3}}{r^2}$

Negative sign shows the attraction force

The equilibrium position,

The both forces are in balance

$F=F'$

$\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q_{1}q_{3}}{(2r)^2}=-\dfrac{1}{4\pi\epsilon_{0}}\times\dfrac{q_{2}q_{3}}{r^2}$

$\dfrac{q_{1}}{4}=q_{2}$

$q_{1}=-4q_{2}$

Hence, The charge of q₁ has the magnitude four times of charge q₂ and sign as that of q₃.