Question

Two identical charges,2.0m apart,exert forces of magnitude 4.0 N on each other.What is the value of either charge?

Answer 1

`\large \boxed{42\, \mu \text{C}}$`

Step-by-step explanation:

The formula for the force exerted between two charges is

`F=k ( q_1q_2)/(r^2)`

where k is the Coulomb constant.

The charges are identical, so we can write the formula as

`F=k(q^(2))/(r^2)`

`\begin{array}{rcl}\text{4.0 N}& = & 8.988 * 10^(9)\text{ N$\cdot$m$^(2)$C$^(-2)$} * \frac{q^(2)}{\text{(2.0 m)}^(2)}\\\\4.0 & = & 2.25 * 10^(9)\text{ C$^(-2)$} * q^(2)\\\\q^(2) & = & \frac{4.0}{2.25 * 10^(9)\text{ C$^(-2)$}}\\\\& = & 1.78 * 10^(-9) \text{ C}^(2)\\q & = & 4.2 * 10^(-5) \text{ C}\\& = & 42\, \mu \text{C}\\\end{array}\\\text{Each charge has a value of $\large \boxed{\mathbf{42\, \mu }\textbf{C}}$}`