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  • Help me understand! - Two electric dipoles, A, B with respective dipole moments are placed on the x-axis with a separati - Electrostatics - JEE Main

Two electric dipoles, A, B with respective dipole moments \vec{d}_{A}qa\hat{i}\: and\: \vec{d}_{B }=-2 qa\hat{i} are placed on the x-axis with a separation R, as shown in the figure 

The distance from A at which both of them production the same potentials is:

  • Option 1)

            \frac{R}{\sqrt{2}+1}

      

      

      

  • Option 2)

    \frac{\sqrt{2}R}{\sqrt{2}+1}

  • Option 3)

    \frac{R}{\sqrt{2}-1}

  • Option 4)

    \frac{\sqrt{2}R}{\sqrt{2}-1}

Answers (1)

best_answer

 

Electric Field and Potential due to an Electric Dipole -

At axial point

E_{axial}=\frac{2kpr}{\left ( r^{2}-l^{2} \right )^{2}}

V_{axial}=\frac{kP}{\left ( r^{2}-l^{2} \right )}

- wherein

 

let at P

       V_{net}=0\\\\V_{net}=V_{1}+V_{2}=0\\\\\frac{K\left ( 4Q_{a} \right )}{x^{2}}-\frac{K\left ( 2Q_{a} \right )}{\left ( R-x \right )^{2}}=0\\\\\Rightarrow x^{2}=2\left ( R-x \right )^{2}\\\\x=\pm \sqrt{2}\left ( R-x \right )\\\\for \; \; x=\sqrt{2}\left ( R-x \right )\\\\\Rightarrow x=\frac{\sqrt{2R}}{\sqrt{2+1}}


Option 1)

        \frac{R}{\sqrt{2}+1}

  

  

  

Option 2)

\frac{\sqrt{2}R}{\sqrt{2}+1}

Option 3)

\frac{R}{\sqrt{2}-1}

Option 4)

\frac{\sqrt{2}R}{\sqrt{2}-1}

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