Question

An electric dipole coincides on the z-axis and its centre coincides with the origin of the cartesian coordinate system. The electric field at an axial point at a distance $z$ from the origin is $E\left(z\right)$ and the electric field at an equatorial point at a distance $y$ from the origin is $E\left(y\right)$.
Given that $y=z>>a$, the value of$\frac{E\left(z\right)}{E\left(y\right)}$ is

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

The correct option is B $2$

For a point on the axis of dipole, field is given by $E\left(z\right)=\frac{2p}{4\pi {ϵ}_o{z}^3}$

For a point on an equatorial point , field $E\left(y\right)=\frac{p}{4\pi {ϵ}_o{y}^3}$

$\frac{E\left(z\right)}{E\left(y\right)}=\frac{2y^3}{z^3}$

Since, $y=z$

Hence,$\frac{E\left(z\right)}{E\left(y\right)}=2$

Answer-(B)