Two electric dipoles, A, B with respective dipole moments vecdA = - 4 qa hati and vecdB = - 2 qa hati 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 :

Question

Two electric dipoles, A, B with respective dipole moments vecdA = - 4 qa hati and vecdB = - 2 qa hati 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 : (A) (√2R/√2+1) (B) (R/√2 +1) (C) (√2R/√2 - 1) (D) (R/√2 -1 )

Tardigrade Admin · Accepted Answer

V = (4qa/(R+x)) = (2qa/(x2)) √2x =R +x x = (R/√2 -1) dist =(R/√2-1) +R = (√2R/√2-1)

Q. Two electric dipoles, $A, B$ with respective dipole moments $d_{A} = - 4 q a \hat{i}$ and $d_{B} = - 2 q a \hat{i}$ 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 :

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

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

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

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

$V = \frac{4 q a}{( R + x )} = \frac{2 q a}{( x ^{2} )}$
$2 x = R + x$
$x = \frac{R}{2 - 1}$
$d i s t = \frac{R}{2 - 1} + R = \frac{2 R}{2 - 1}$

Q. Two electric dipoles, A,B with respective dipole moments dA​=−4qai^ and dB​=−2qai^ 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 :

2​+12​R​

2​+1R​

2​−12​R​

2​−1R​