Question

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Solution

Electric dipole moment is the product of either charges or the distance between two equal and opposite charges.

It is a vector quantity.
Electric dipole moment at a point on the equatorial plane:

Consider a point P on broad side on the position of dipole formed of charges + q and - q at separation 2l. The distance of point P from mid-point O of electric dipole is r.

Let E₁ and E₂ be the electric field strength due to charges +q and –q of electric dipole.

From the fig. we have
$Error converting from MathML to accessible text.$
Now, inorder to find the resultant electric field, we resolve the components along and perpendicular to AB.
The components perpendicular to AB are sin components and they being equal and opposite to each other cancel each other.

Therefore,

Resultant electric field is given by,
E₁ = E₁ $cos space theta space plus space E subscript 2 space c o s space theta$

But,
$Error converting from MathML to accessible text.$

From the fig. we can see that,
$Error converting from MathML to accessible text.$

If dipole is infinitesimal and point P is far away, then l² can be neglected as compared to r².

Therefore,
$straight E space equals space fraction numerator 1 over denominator 4 πε subscript straight o end fraction space straight p over straight r cubed comma space parallel space to space BA with rightwards harpoon with barb upwards on top$

b) Equipotential surfaces due to an electric dipole is given by,

Electric potential is zero at all points in the plane passing through the dipole equator.

For Daily Free Study Material Join wiredfaculty

Electrostatic Potential And Capacitance

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Some More Questions From Electrostatic Potential and Capacitance Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Electrostatic Potential And Capacitance

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole. (b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Some More Questions From Electrostatic Potential and Capacitance Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.