An electric dipole of dipole moment vec{p} is | vedclass

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(D) The electric potential $V$ due to an electric dipole at a point $(r, 	heta)$ is given by $V = \frac{p \cos 	heta}{4 \pi \varepsilon_0 r^2}$.Poin

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$\frac{p q}{4 \pi \varepsilon_0 a^2}$

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(D) The electric potential $V$ due to an electric dipole at a point $(r, 	heta)$ is given by $V = \frac{p \cos 	heta}{4 \pi \varepsilon_0 r^2}$.Point $A(a, 0, 0)$ lies on the equatorial plane of the dipole (which is along the $z$-axis),so the angle $	heta_A = 90^{\circ}$. Thus,the potential at $A$ is $V_A = \frac{p \cos 90^{\circ}}{4 \pi \varepsilon_0 a^2} = 0$.Point $B(0, 0, a)$ lies on the axial line of the dipole,so the angle $	heta_B = 0^{\circ}$. Thus,the potential at $B$ is $V_B = \frac{p \cos 0^{\circ}}{4 \pi \varepsilon_0 a^2} = \frac{p}{4 \pi \varepsilon_0 a^2}$.The work done $W$ to move a charge $q$ from $A$ to $B$ is $W = q(V_B - V_A)$.Substituting the values,$W = q \left( \frac{p}{4 \pi \varepsilon_0 a^2} - 0 ight) = \frac{p q}{4 \pi \varepsilon_0 a^2}$.

An electric dipole of dipole moment $\vec{p}$ is placed at the origin of the coordinate system along the $z$-axis. The amount of work required to move a charge $q$ from the point $A(a, 0, 0)$ to the point $B(0, 0, a)$ is,

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