Electric Potential Energy — Question 1

Question 1

A negative charge moved along the field gains electric potential energy

A charge $q=-3.00\,\mu$C is moved from A to B through displacement $.200\hat{\mathbf x}$ m in the uniform static field $\mathbf E=400\hat{\mathbf x}$ N/C. Other forces are absent except an external actuator.

1. Find electric work and the change in electric potential energy.

2. Find actuator work if the motion is quasistatic, and explain the direction of the actuator force.

Question 1 - Solution

A negative charge moved along the field gains electric potential energy

(a) Method and calculation

$$W_e=q\mathbf E\cdot\Delta\mathbf r=(-3.00\times10^{-6})(400)(.200)=-240\,\mu\mathrm J.$$$$\Delta U=-W_e=+240\,\mu\mathrm J.$$

(b) Interpretation and further calculation

$$\Delta K=W_e+W_{\mathrm{ext}}=0\Rightarrow W_{\mathrm{ext}}=+240\,\mu\mathrm J.$$$$\mathbf F_{\mathrm{ext}}=-q\mathbf E=+1.20\times10^{-3}\hat{\mathbf x}\,\mathrm N.$$The negative charge is pushed against its electric force even though its displacement follows the field.

Physical check

Field direction gives the force direction for a positive charge; the specified negative charge reverses that force.