Two electric dipoles of moments p and 27 p ar | vedclass

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Question

(A) Let the two dipoles be placed at points $A$ and $B$ with dipole moments $p_1 = p$ and $p_2 = 27 p$ respectively,oriented in opposite directions.Le

Vedclass · Accepted Answer

$6 \,cm$

Vedclass · Answer

(A) Let the two dipoles be placed at points $A$ and $B$ with dipole moments $p_1 = p$ and $p_2 = 27 p$ respectively,oriented in opposite directions.Let $P$ be the null point between them where the net electric field intensity is zero.Let $x$ be the distance of point $P$ from the dipole at $A$.The distance of point $P$ from the dipole at $B$ is $(24 - x) \,cm$.The electric field intensity on the axial line of a short electric dipole is given by $E = \frac{2kp}{r^3}$.For the net electric field to be zero at point $P$,the magnitudes of the electric fields produced by both dipoles must be equal: $E_1 = E_2$.Substituting the values,we get:$\frac{2kp}{x^3} = \frac{2k(27p)}{(24 - x)^3}$$\frac{1}{x^3} = \frac{27}{(24 - x)^3}$Taking the cube root on both sides:$\frac{1}{x} = \frac{3}{24 - x}$$24 - x = 3x$$24 = 4x$$x = 6 \,cm$.Thus,the electric field is zero at a distance of $6 \,cm$ from the dipole of moment $p$.

Two electric dipoles of moments $p$ and $27 p$ are placed in opposite directions on a line at a distance of $24 \,cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $p$ is

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