By using Coulomb's law, we want to find the value of q₁ given that q₂ experiences no net electric force. We will find that q₁ = 8nC
Working with Coulomb's law.
Coulomb's law says that for two charges q₁ and q₂ separated by a distance r, the force that each one experiences is:
[tex]F = k\frac{q_1*q_2}{r^2}[/tex]
Where k is a constant
Here we can see that q₂ interacts with two charges, then the total force on q₂ will be:
[tex]F = k\frac{q_1*q_2}{(20cm)^2} + k\frac{-2nC*q_2}{(10cm)^2}[/tex]
And we know that it must be equal to zero, so we can write it as:
[tex]F = k\frac{q_1*q_2}{(20cm)^2} + k\frac{-2nC*q_2}{(10cm)^2} = 0\\\\k*q_2*(\frac{q_1}{(20cm)^2} + \frac{-2nC}{(10cm)^2}) = 0\\[/tex]
The parenthesis must be equal to zero, so we can write:
[tex]\frac{q_1}{(20cm)^2} + \frac{-2nC}{(10cm)^2} = 0[/tex]
And now we can solve this for q₁ to get:
[tex]q_1 = 2nC*(\frac{(20cm)^2}{(10cm)^2} ) = 8nC[/tex]
If you want to learn more about Coulomb's law, you can read:
https://brainly.com/question/24743340
