Convert ESU of charge to EMU of charge
Learn how to convert
1
ESU of charge to
EMU of charge
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(ESU \text{ } of \text{ } charge\right)={\color{rgb(20,165,174)} x}\left(EMU \text{ } of \text{ } charge\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(coulomb\right)\)
\(\text{Left side: 1.0 } \left(ESU \text{ } of \text{ } charge\right) = {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}\left(coulomb\right)} = {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}\left(C\right)}\)
\(\text{Right side: 1.0 } \left(EMU \text{ } of \text{ } charge\right) = {\color{rgb(125,164,120)} 10.0\left(coulomb\right)} = {\color{rgb(125,164,120)} 10.0\left(C\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(ESU \text{ } of \text{ } charge\right)={\color{rgb(20,165,174)} x}\left(EMU \text{ } of \text{ } charge\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}} \times {\color{rgb(89,182,91)} \left(coulomb\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10.0}} \times {\color{rgb(125,164,120)} \left(coulomb\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}} \cdot {\color{rgb(89,182,91)} \left(C\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10.0} \cdot {\color{rgb(125,164,120)} \left(C\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 3.33564 \times 10^{-10}} \cdot {\color{rgb(89,182,91)} \cancel{\left(C\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10.0} \times {\color{rgb(125,164,120)} \cancel{\left(C\right)}}\)
\(\text{Conversion Equation}\)
\(3.33564 \times 10^{-10} = {\color{rgb(20,165,174)} x} \times 10.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10.0 = 3.33564 \times 10^{-10}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 10.0 \times \dfrac{1.0}{10.0} = 3.33564 \times 10^{-10} \times \dfrac{1.0}{10.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10.0}}} = 3.33564 \times 10^{-10} \times \dfrac{1.0}{10.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.33564 \times 10^{-10}}{10.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 3.33564 \times 10^{-11}\approx3.3356 \times 10^{-11}\)
\(\text{Conversion Equation}\)
\(1.0\left(ESU \text{ } of \text{ } charge\right)\approx{\color{rgb(20,165,174)} 3.3356 \times 10^{-11}}\left(EMU \text{ } of \text{ } charge\right)\)
