For a short dipole placed at origin O,the dip | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Point $A$ is on the axial line of the dipole at distance $r$. The electric potential $V_A$ and electric field $E_A$ are given by:$V_A = \frac{kP}{

Vedclass · Accepted Answer

zero and $\frac{E_0}{16}$

Vedclass · Answer

(C) Point $A$ is on the axial line of the dipole at distance $r$. The electric potential $V_A$ and electric field $E_A$ are given by:$V_A = \frac{kP}{r^2} = V_0$$E_A = \frac{2kP}{r^3} = E_0$Point $B$ is on the equatorial line of the dipole at distance $2r$. The electric potential $V_B$ at any point on the equatorial line is zero because the potential is given by $V = \frac{k \vec{P} \cdot \hat{r}}{r^2}$,and for the equatorial line,the angle between $\vec{P}$ and the position vector $\vec{r}$ is $90^\circ$,so $\cos(90^\circ) = 0$.The electric field $E_B$ on the equatorial line at distance $d = 2r$ is given by:$E_B = \frac{kP}{d^3} = \frac{kP}{(2r)^3} = \frac{kP}{8r^3}$Since $E_0 = \frac{2kP}{r^3}$,we have $\frac{kP}{r^3} = \frac{E_0}{2}$.Substituting this into the expression for $E_B$:$E_B = \frac{1}{8} 	imes \left( \frac{kP}{r^3} ight) = \frac{1}{8} 	imes \frac{E_0}{2} = \frac{E_0}{16}$.Thus,the potential is zero and the electric field is $\frac{E_0}{16}$.

Similar Questions

Torque acting on an electric dipole in a uniform electric field is maximum when the angle between $\vec{p}$ and $\vec{E}$ is . . . . . . . (in $^{\circ}$)

Two electric dipoles of moment $P$ and $27 P$ are placed on a line with their centres $24 \,cm$ apart. Their dipole moments are in opposite directions. At which point between the dipoles, measured from the centre of the dipole of moment $P$, will the electric field be zero (in $\,cm$)?

Two point charges $-4 \mu C$ and $4 \mu C$,constituting an electric dipole,are placed at $(-9, 0, 0) \ cm$ and $(9, 0, 0) \ cm$ in a uniform electric field of strength $10^4 \ NC^{-1}$. The work done on the dipole in rotating it from the equilibrium position through $180^{\circ}$ is: (in $mJ$)

The direction of the electric field at a point on the equatorial line of an electric dipole is .......

The force on a charge situated on the axis of a dipole is $F$. If the charge is shifted to double the distance,the new force will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module