## Related questions with answers

(a) In Gaussian units, show that the square of a potential difference $\left(\phi_{2}-\phi_{1}\right)^{2}$ has the same dimensions as force. (In SI units, $\epsilon_{0}\left(\phi_{2}-\phi_{1}\right)^{2}$ has the same units as force.) This tells us that the electrostatic forces between bodies will largely be determined, as to order of magnitude, by the potential differences involved. Dimensions will enter only in ratios, and there may be some constants like $4 \pi$. What is the order of magnitude of force you expect with 1 statvolt potential difference between something and something else? (b) Practically achievable potential differences are rather severely limited, for reasons having to do with the structure of matter. The highest man-made difference of electric potential is about $10^{7}$ volts, achieved by a Van de Graaff electrostatic generator operating under high pressure. (Billion-volt accelerators do not involve potential differences that large.) How many pounds force are you likely to find associated with a “square megavolt”? These considerationsmay suggestwhy electrostatic motors have not found much application.

Solution

Verified$\textbf{Part(a)}$

$(\phi)^2\sim\left(\dfrac{Q^2}{d^2}\right)\sim F$

Where

$\phi$ is the potential field resulted from the given charge .

$Q$ is the charge .

$d$ is the distance from the charge .

$(1\;\text{statvolt})^2=\dfrac{(1\;esu)^2}{(1 cm)^2}=1\;\text{dyne}$

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