Consider a system of three charges \[\frac{q}{3},\frac{q}{3}\] and \[\frac{2q}{3}\] placed at points A, B and C, respectively, as shown in figure. Take 0 to be the centre of circle of radius R and angle CAB =  . Choose the correct one: |
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A) The electric field at point \[{\mathrm O}\]is \[\frac{q}{8\pi {{\in }_{0}}{{R}^{2}}}\] directed along the negative x-axis.
B) The potential energy of the system is zero.
C) The magnitude of the force between the charges at \[C\]and \[B\]is \[\frac{{{q}^{2}}}{54\pi {{\in }_{0}}{{R}^{2}}}\]
D) The potential at points O is \[\frac{q}{12\pi {{\in }_{0}}{{R}^{{}}}}\]
Correct Answer: C
Solution :
| electric field at the Centre, \[E=\frac{1}{4\pi {{\in }_{0}}}\frac{\left( 2q/3 \right)}{{{R}^{2}}}=\frac{q}{6\pi {{\in }_{0}}{{R}^{2}}}\] |
| Potential energy of this system, \[U=\frac{1}{4\pi {{\in }_{0}}}\left[ \frac{\frac{q}{3}\times \frac{q}{3}}{2R}+\frac{\frac{q}{3}\left( -\frac{2q}{3} \right)}{\sqrt{3R}}+\frac{\frac{q}{3}\left( -\frac{2q}{3} \right)}{R} \right]\ne 0\] |
| Force, \[{{F}_{BC}}=\frac{1}{4\pi {{\in }_{0}}}\left[ \frac{\frac{q}{3}\times \left( \frac{2q}{3} \right)}{{{\left( \sqrt{3R} \right)}^{2}}} \right]\]\[=\frac{{{q}^{2}}}{54\pi {{\in }_{0}}{{R}^{2}}}\] |
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