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.
The equation is the following:
where is the charge of the particle. Thus, the graph will be the straight line with slope . Using Excel and the linear approximation, obtain the slope.
Let's account for units:
Thus, obtain:
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