From potential to charge

Inverse: from potential to charge. A point located at $r = 50\ \text{cm}$ from an isolated point charge has potential $V = -3{,}6\ \text{kV}$. Determine the value and sign of the charge.

Solution

Setting up. The potential of a point charge is $V = \dfrac{kQ}{r}$. Inverting for the charge: $Q = \frac{V\,r}{k}$ Data. $V = -3{,}6 \text{ kV} = -3{,}6\cdot 10^3$ V, $r = 50 \text{ cm} = 0{,}50$ m, $k = 9\cdot 10^9$. Substitution. $Q = \frac{(-3{,}6\cdot 10^3)(0{,}50)}{9\cdot 10^9} = \frac{-1{,}8\cdot 10^3}{9\cdot 10^9}$ Result. $\ev{Q \approx -2\cdot 10^{-7} \ \text{C} = -200 \ \text{nC}}$ The negative potential immediately reveals the negative sign of the charge: a negative charge lowers the potential around itself.

Connections

Topics: Electric field and potential Concepts: Electric potential · Electric charge Skills: Superposition principle Methods: Gradient method Objects: Charged sphere