Question

Two identical copper spheres A and B equally charged, repel each other with a force of $4\times {10}^{-5}N$. A third similar copper sphere C carrying no charge is now brought into contact with A and placed mid-way between A and B. What force would C experience?

Answer 1

As we know,

$f=k\frac{q^2}{d^2}$

$f_{net}=f_a-f_b$

$f_{net}=\frac{k\left(\frac{q}{2}\right)\left(\frac{q}{2}\right)}{\left(\frac{d}{2}\right)}$-$\frac{kq\left(\frac{q}{2}\right)}{{\left(\frac{d}{2}\right)}^2}$

$f_{net}=\frac{\frac{k{q}^2}{4}}{\frac{d^2}{4}}-\frac{\frac{k{q}^2}{2}}{\frac{d^2}{4}}$

$f_{net}=\frac{k{q}^2}{d^2}(1-2)$

$f_{net}=-\frac{k{q}^2}{d^2}$ towards left