Answer to Question #249123 in Electric Circuits for BENSON

Question

Define a uniform electric field (E), and derive its work done in a moving charge (q) through a

distance (d)?

Answer 1

We will be able to find the work done as the integral of the point-product between the force and displacement vectors since they both exist on the same dimension (x-axis) and we proceed to substitute the force F as the electrical force (F_elec = qE) and the total displacement as Δl = d. With that information we find the work done as

$W=\int{ \overrightarrow{F}\cdot \overrightarrow{dl} }=\int{F\cdot {dl}}=F_{elec}\cdot \Delta l \\ \therefore W=qEd$

In conclusion, the work done in moving a charge q in an electric field E through a distance d is equal to $W=qEd$.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.