Electric Potential — Question 3

Question 3

Several probe energies identify one source potential

With a common energy reference and fixed sources, probes at P have $(q,U)=(2.00\,\mathrm{nC},30.0\,\mathrm{nJ})$ and $(-3.00\,\mathrm{nC},-45.0\,\mathrm{nJ})$. Probe interactions and source motion are negligible.

1. Determine whether both measurements give the same potential.

2. Find the charge of a third probe with energy $-60.0$ nJ at P and its energy change on transfer to a point with potential 5.00 V.

Question 3 - Solution

Several probe energies identify one source potential

(a) Method and calculation

$$V_P=U_1/q_1=30.0/2.00=15.0\,\mathrm V.$$$$U_2/q_2=(-45.0)/(-3.00)=15.0\,\mathrm V.$$

(b) Interpretation and further calculation

$$q_3=U_3/V_P=-4.00\,\mathrm{nC}.$$$$\Delta U_3=q_3(5.00-15.0)=+40.0\,\mathrm{nJ}.$$

Physical check

The proportionality U=qV requires the same reference and a probe that does not alter the source potential.