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A dipole of dipole moment is kept at the origin of coordinates. At which of the following points can the clectric field be :

A dipole of dipole moment 10−9Cmi^ is kept at the origin of coordinate
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Q. 12. What is common potential ? Derive an expression for the loss of energy on sharing of charges between the conductors. Ans. When two conductors of different capacitances and charged to different potentials are (P.S.E.B. 2010) connected by a metallic wire, charge flow from a conductor at higher potential to the conductor at lower potential till potential of both the conductors becomes equal, this is called common potential. \[ \begin{aligned} q_{1}+q_{2} & =q \\ \therefore \quad \mathrm{C}_{1} \mathrm{~V}_{1}+\mathrm{C}_{2} \mathrm{~V}_{2} & =\left(\mathrm{C}_{1}+\mathrm{C}_{2}\right) \mathrm{V} \quad\left[\because \mathrm{C}=\frac{q}{\mathrm{~V}}\right] \end{aligned} \] Here, common potential Here, \[ \begin{array}{l} \mathrm{U}^{\prime}=\frac{1}{2} \mathrm{C}_{1} \mathrm{~V}^{2}+\frac{1}{2} \mathrm{C}_{2} \mathrm{v}^{2} \\ \text { Loss of Energy }=\mathrm{U}-\mathrm{U}^{\prime} \\ =\left(\frac{1}{2} C_{1} V_{1}^{2}+\frac{1}{2} C_{2} V_{2}^{2}\right)-\left(\frac{1}{2} C_{1} V^{2}+\frac{1}{2} C_{2} V^{2}\right) \\ =\frac{1}{2} C_{1} V_{1}^{2}+\frac{1}{2} C_{2} V_{2}^{2}-\frac{1}{2}\left(C_{1}+C_{2}\right) V^{2} \\ =\frac{1}{2} C_{1} V_{1}^{2}+\frac{1}{2} C_{2} V_{2}^{2}-\frac{1}{2}\left(C_{1}+C_{2}\right)\left(\frac{C_{1} V_{1}+C_{2} V_{2}}{C_{1}+C_{2}}\right)^{2} \\ =\frac{1}{2} C_{1} V_{1}^{2}+\frac{1}{2} C_{2} V_{2}^{2}-\left(C_{1}+C_{2}\right) \frac{\left[C_{1}^{2} V_{1}^{2}+C_{2}^{2} V_{2}^{2}+2 C_{1} C_{2} V_{1} V_{2}\right]}{2\left(C_{1}+C_{2}\right)^{2}} \\ =\frac{1}{2} C_{1} V_{1}^{2}+\frac{1}{2} C_{2} V_{2}^{2}-\frac{\left[C_{1}^{2} V_{1}^{2}+C_{2}^{2} V_{2}^{2}+2 C_{1} C_{2} V_{1} V_{2}\right]}{2\left(C_{1}+C_{2}\right)} \\ =\frac{C_{1} V_{1}^{2}\left(C_{1}+C_{2}\right)+C_{2} V_{2}^{2}\left(C_{1}+C_{2}\right)-C_{1}^{2} V_{1}^{2}-C_{2}^{2} V_{2}^{2}-2 C_{1} C_{2} V_{1} V_{2}}{2\left(C_{1}+C_{2}\right)} \\ =\frac{C_{1}^{2} V_{1}^{2}+C_{1} C_{2} V_{1}^{2}+C_{1} C_{2} V_{2}^{2}+C_{2}^{2} V_{2}^{2}-C_{1}^{2} V_{1}^{2}-C_{2}^{2} V_{2}^{2}-2 C_{1} C_{2} V_{1} V_{2}}{2\left(C_{1}+C_{2}\right)} \\ \end{array} \]
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Question Text
A dipole of dipole moment is kept at the origin of coordinates. At which of the following points can the clectric field be :
Updated OnJul 14, 2022
TopicElectrostats
SubjectPhysics
ClassClass 12
Answer Type Video solution: 1
Upvotes74
Avg. Video Duration9 min