JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
A system of three charges are placed as shown in the figure. If \(D > > d,\) the potential energy of the system is best given \(b\)
- A \(\frac{1}{{4\pi {\varepsilon _0}}}\left[ { - \frac{{{q^2}}}{d} - \frac{{qQd}}{{{D^2}}}} \right]\)
- B \(\frac{1}{{4\pi {\varepsilon _0}}}\left[ { - \frac{{{q^2}}}{d} - \frac{{qQd}}{{{2D^2}}}} \right]\)
- C \(\frac{1}{{4\pi {\varepsilon _0}}}\left[ { - \frac{{{q^2}}}{d} + \frac{{2qQd}}{{{D^2}}}} \right]\)
- D \(\frac{1}{{4\pi {\varepsilon _0}}}\left[ { + \frac{{{q^2}}}{d} - \frac{{qQd}}{{{D^2}}}} \right]\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{{4\pi {\varepsilon _0}}}\left[ { + \frac{{{q^2}}}{d} - \frac{{qQd}}{{{D^2}}}} \right]\)
Step-by-step Solution
Detailed explanation
\(U_{total}\) \(=\) \(U_{self\,of\, dipole} + U_{interaction}\) \(=-\frac{k q^{2}}{d}-\left(\frac{k Q}{D^{2}}\right) q d\) \(=-k\left[\frac{q^{2}}{d}+\frac{q Q d}{D^{2}}\right]\)
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