Question

A region surrounding a stationary electric dipole has ______.
A. magnetic field
B. electric field only
C. both electric and magnetic fields
D. no electric field and magnetic fields.

Answer 1

Hint: A moving charge constitutes electric current because the electric current is defined as the rate of flow of charge per unit of time. To find the electric field around a charge or group of charges we can use the Gauss law of electrostatics and to find the magnetic field around a charge or group of charges we can use Ampere’s circuital law.

Complete step by step solution:
An electric dipole is the arrangement of two charges of equal magnitude and opposite in nature separated by a very small distance. Using Ampere’s circuital law, the magnetic field around an electric current is given as,
$\oint B.dl=\mu_o I_{in}$
Here, if we find the line integral around the electric field then the magnitude of the magnetic field is proportional to the electric current enclosed within the closed path.

As we know that electric current is the rate of flow of charge, i.e. \[I = \dfrac{{dq}}{{dt}}\], but in the given question the electric dipoles are stationary so the electric current enclosed will be zero. Hence, a region surrounding a stationary electric dipole hasn’t magnetic field.

Using Coulomb’s law of electrostatics, the electric field at a point due to a given charge is,
\[\overrightarrow E = \dfrac{Q}{{4\pi {\varepsilon _0}}}\left( {\dfrac{{\overrightarrow r }}{{{r^3}}}} \right)\]
Here \[\overrightarrow r \] is the position vector of the point where we need to find the electric field.

As the position vector with respect to both the charges will be different so the net electric field will be non-zero.
\[\overrightarrow E = \overrightarrow {{E_ + }} + \overrightarrow {{E_ - }} \]
\[\Rightarrow \overrightarrow E = \dfrac{Q}{{4\pi {\varepsilon _0}}}\left( {\dfrac{{\overrightarrow {{r_ + }} }}{{r_ + ^3}}} \right) - \dfrac{Q}{{4\pi {\varepsilon _0}}}\left( {\dfrac{{\overrightarrow {{r_ - }} }}{{r_ - ^3}}} \right) \ne 0\]
Hence, a region surrounding a stationary electric dipole has an electric field. So, a region surrounding a stationary electric dipole has only an electric field.

Therefore, the correct option is B.

Note: If the distance between the charges is insignificant to the distance of the point in the surrounding with respect to the midpoint of the charges then using Gauss law the electric field also becomes zero when we consider the charges individually.