Question

What will be the answer of the above question?​

Answer 1

Answer:

Possible value of q₁ and q₂ are 2 μC and 8 μC.

Explanation:

Since, potential energy formula is

$U = \frac{1}{4\pi e_{o}}\frac{q_{1}q_{2}}{r}$

We can find q₁q₂, which will come out to be 1.6 × 10⁻¹¹

Now,

q₁ + q₂ = 10 × 10⁻⁶

⇒ q₁ = 10⁻⁵ - q₂

Hence,

$q_{1}q_{2}~=~1.6*10^{-11}\\\\q_{2}*(10^{-5}-q_{2})=~~~~~1.6*10^{-11}\\\\=10^{-5}q_{2}~~-~~q_{2}^{2}~~=~~~~~0.16*10^{-10}\\\\=q_{2}^{2}~-~10^{-5}q_{2}~+~0.16*10^{-10}=0\\\\=q_{2}^{2}-0.8*10^{-5}q_{2}-0.2*10^{-5}q_{2}~+~0.16*10^{-10} = 0\\\\=q_{2}(q_{2}-0.8*10^{-5})-0.2*10^{-5}(q_{2}-0.8*10^{-5})~=~0\\\\=(q_{2}-0.2*10^{-5})*(q_{2}-0.8*10^{-5})~=~0$

Either q₂ = 0.2 × 10⁻⁵ = 2 μC   or   q₂ = 0.8 × 10⁻⁵ = 8 μC

Both can be true.