Question 58: Electrostatics & Capacitance

Question

Three point charges $-1 C,+1 C,+1 C$ are placed at points $A, B, C$ respectively of a triangle $A B C$. What is the total potential energy of the system? [given $\mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm}$ and $\mathrm{BC}=3 \mathrm{~cm}$ ]

Accepted Answer

Let $q_A=-1m\,C$, $q_B=+1m\,C$, $q_C=+1m\,C$, with
AB = AC = 0.06 m, BC = 0.03 m, and $k=8.99	imes10^9m\,Nm^2/C^2$.
Pairwise energies
Ã¢ÂÂ¢ $U_{AB}=k\frac{q_Aq_B}{AB}=8.99	imes10^9\frac{-1\cdot1}{0.06}=-1.4983	imes10^{11}m\,J$
Ã¢ÂÂ¢ $U_{AC}=k\frac{q_Aq_C}{AC}=-1.4983	imes10^{11}m\,J$
Ã¢ÂÂ¢ $U_{BC}=k\frac{q_Bq_C}{BC}=8.99	imes10^9\frac{1\cdot1}{0.03}=2.9967	imes10^{11}m\,J$
Total energy
$      U_{m tot}=U_{AB}+U_{AC}+U_{BC}                =-1.4983	imes10^{11}-1.4983	imes10^{11}+2.9967	imes10^{11}                =0\;m J.    $
Answer: 0 J (Option A).

Answer

0 J (Zero joule)

Answer

$4.5 	imes 10^{13} \mathrm{~J}$

Answer

$6 	imes 10^{13} J$

Answer

$3 	imes 10^{13} J$

Electrostatics & Capacitance

Three point charges -1 C,+1 C,+1 C are placed at points A, B, C respectively of a triangle A B C. What is the total potential energy of the system? [given \mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm} and \mathrm{BC}=3 \mathrm{~cm} ]

Choose the correct answer: