Physics 2Electric Potential Energy Problems

*\( W=F \cdot d=q_0 E d=U \)*

*\( U=\frac{1}{4 \pi \varepsilon_{0}} \frac{q q_{0}}{r} \)*

*\( U=\frac{1}{4 \pi \varepsilon_0} \frac{e^{2}}{r} \)*

\( \left(e=1.60 * 10^{-14} c\right) \)

A point charge \(q_{1}=+2.40 \mu \mathrm{C}\) is held stationary at the
origin. A second point charge \(q_{2}=-4.30 \mu \mathrm{C}\) moves from
the point \(x=0.150 \mathrm{m}, \quad y=0\) to the point \(x=0.250 \mathrm{m}\) ,
\(y=0.250 \mathrm{m} .\) How much work is done by the electric force on \(q_{2} ?\)

\( W_{a \rightarrow b}=U_{a}-U_{b} \)

\( U_{a}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r_{a}} \)

      \( =9 * 10^{9} * \frac{2.4 * 10^{-6} *-4 \cdot 3 * 10^{-6}}{0.15} \)

       \( =-0.6184 \mathrm{J} \)

\( U_{b}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r_{b}} \)

     \( =9 * 10^{9} * \quad \frac{2 \cdot 4 * 10^{-6} *-4 \cdot 3*10^{-6}}{0.3536} \)

      \( =-0.26235J \)

Three equal \(1.20-\mu \mathrm{C}\) point charges are placed at the
corners of an equilateral triangle whose sides are 0.500 m long.
What is the potential energy of the system? (Take as zero the
potential energy of the three charges when they are infinitely
far apart.)

\( U=U_{12}+U_{13}+U_{23} \)

   \( =U_{12}=U_{13}=U_{23} \)

\( U=\frac{3 k q^{2}}{0.5} =\frac{3 * K *\left(1.2 * 10^{-6}\right)^{2}}{0.5} \)

                \( =0.078 J \)