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Four point charges of magnitudes +2 \mu C,+2 \mu C,-2 \mu C and  -2 \mu C respectively are placed at the corners A, B, C, D of a square having each side as 0.2 \mathrm{~m}. Calculate work done in moving an electron from the intersection point of the diagonals A C and B D to the middle point of \mathrm{BC}.

Option: 1

0
 


Option: 2

7 Joules
 


Option: 3

16 Joules
 


Option: 4

None of the above.


Answers (1)

best_answer

Let the charges be placed clockwise at the corners of above diagram.

Each side =\mathrm{a}=0.2 \mathrm{~m} \text {. }

\begin{gathered} B D=A C=\sqrt{a^2+a^2}=a \sqrt{2} \\ O A=O C=O B=O D=\frac{a}{\sqrt{2}} \end{gathered}

Potential at O;

    V_o=\frac{1}{4 \pi \epsilon_o}\left[\frac{2 \times 10^{-6}}{O A}+\frac{2 \times 10^{-6}}{O B}-\frac{2 \times 10^{-6}}{O C}-\frac{2 \times 10^{-6}}{O D}\right]

V_o=0

Also,

A E=D E=a \frac{\sqrt{5}}{2}

Potential at E;

V_E=\frac{1}{4 \pi \epsilon_o}\left[\frac{2 \times 10^{-6}}{A E}+\frac{2 \times 10^{-6}}{B E}-\frac{2 \times 10^{-6}}{C E}-\frac{2 \times 10^{-6}}{D E}\right]

V_E=0

Work done =-\mathrm{e}[\mathrm{V}$ (final) $-\mathrm{V}($ initial) $]
Hence, Work done =0

Posted by

Riya

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