Question:
Two electric dipoles, $A, B$ with respective dipole moments $\vec{d}_A = - 4 \,qa \,\hat{i}$ and $\vec{d}_B = - 2 \,qa\, \hat{i}$ placed on the x-axis with a separation $R$, as shown in the figure The distance from $A$ at which both of them produce the same potential is :
Two electric dipoles, $A, B$ with respective dipole moments $\vec{d}_A = - 4 \,qa \,\hat{i}$ and $\vec{d}_B = - 2 \,qa\, \hat{i}$ placed on the x-axis with a separation $R$, as shown in the figure The distance from $A$ at which both of them produce the same potential is :
Updated On: Jul 31, 2024
- $\frac{\sqrt{2}R}{\sqrt{2}+1}$
- $\frac{R}{\sqrt{2} +1}$
- $\frac{\sqrt{2}R}{\sqrt{2} - 1}$
- $\frac{R}{\sqrt{2} -1 }$
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The Correct Option is C
Solution and Explanation
$V = \frac{4qa}{\left(R+x\right)} = \frac{2qa}{\left(x^{2}\right)} $
$ \sqrt{2}x =R +x $
$ x = \frac{R}{\sqrt{2} -1} $
$ dist =\frac{R}{\sqrt{2}-1} +R = \frac{\sqrt{2}R}{\sqrt{2}-1}$
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Concepts Used:
Electric Dipole
An electric dipole is a pair of equal and opposite point charges -q and q, separated by a distance of 2a. The direction from q to -q is said to be the direction in space.
p=q×2a
where,
p denotes the electric dipole moment, pointing from the negative charge to the positive charge.
Force Applied on Electric Dipole
