Answer to Question #308243 in Physics for Hana

Question

In a certain region an electric potential V is present. An unknown charge Q is moved around this region between points at potential difference ΔV. A physicist measures the change in the potential energy ΔU as the charge is moved. The table below shows the data of the measurements. The unit for ΔV are MV (mega-Volts), the units for ΔU are kJ (kilo-joules).

ΔV

57.1

29.9

16.7

9.97

8.55

8.32

6.52

6.87

ΔU

362.8

157.6

124.3

55.3

48.8

53.9

37.9

47.3

You want to find the value of the unknown charge Q in mC. Since ΔU = QΔV make the plot 𝑦=𝑚𝑥 where 𝑦=𝛥𝑈 and 𝑥=𝛥𝑉. Use Excel, calculator or whatever you prefer. From the slope of the plot, calculate Q.

Answer 1

The equation is the following:

$$\Delta U = Q\Delta V$$

where $Q$ is the charge of the particle. Thus, the graph will be the straight line with slope $Q$. Using Excel and the linear approximation, obtain the slope.

Let's account for units:

$$[Q] = \dfrac{[\Delta U]}{[\Delta V]} = \dfrac{10^3J}{10^6V} = 10\times 10^{-3}C$$

Thus, obtain:

$$Q = 6.19\times 10^{-3}C$$