Drill – work in moving a charge

Drill: work in moving a charge. A test charge $q = 2\ \text{nC}$ is moved from point A ($V_A = 200\ \text{V}$) to point B ($V_B = 50\ \text{V}$). How much work does the electric field do? Is the work positive or negative?

Solution

Setup. The work done by the field in moving a charge from A to B is $W_\text{campo} = q\,(V_A - V_B)$ Data. $q = 2\ \text{nC} = 2\cdot 10^{-9}$ C, $V_A = 200$ V, $V_B = 50$ V. Substitution. $W_\text{campo} = (2\cdot 10^{-9})\,(200 - 50) = (2\cdot 10^{-9})(150)$ Result. $\ev{W_\text{campo} \approx 3\cdot 10^{-7} \ \text{J} = 0{,}3 \ \mu\text{J}}$ Sign. The work is positive: a positive charge moves spontaneously from a higher potential ($200$ V) to a lower one ($50$ V), so the field “goes along with it” doing positive work, at the expense of its potential energy.

Links

Topics: Electric field and potential Concepts: Electric potential · Electrostatic potential energy Skills: Conservation of energy Methods: Gradient method Objects: Charged sphere