What is the net force acting on a dipole placed in a uniform electric field?

Depends on the magnitude of charges

At a given point, the electric field intensity due to a dipole is the

the vector sum of electric field intensity due to individual charges of the dipole

the algebraic sum of electric field intensity due to individual charges of the dipole

the product of electric field intensity due to individual charges of the dipole

Electric Field Intensity at any point due to an Ideal Dipole Derivation

What is an Electric Field Intensity?

The space around an electric charge in which its influence can be felt is known as the electric field. At a point, the electric field intensity is the force experienced by a unit positive charge placed at that point. The electric field intensity due to a positive charge is always directed away from the charge and the intensity due to a negative charge is always directed towards the charge. Electric field intensity is a vector quantity.

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What is an Electric Dipole?

An electric dipole is defined as a pair of opposite charges q and –q separated by a distance d.

Derivation of Electric Field Intensity for points on the Axial Line of a Dipole

Electric Field Intensity of an Electric Dipole Derivation

Consider a system of charges -q and +q separated by a distance 2a. Let “P” be any point on the axial line where the electric field intensity needs to be determined.

Electric Field at P (E_B) due to +q is given as follows:

\(\begin{array}{l}E_{B}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{BP^2}\end{array} \)

\(\begin{array}{l}E_{B}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{(r-a)^2}\end{array} \)

The electric field at P (E_A) due to -q is given as follows:

\(\begin{array}{l}E_{A}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{(AP)^2}\end{array} \)

\(\begin{array}{l}E_{A}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{(r+a)^2}\end{array} \)

The following equation gives the net field at point P:

\(\begin{array}{l}E_{P}=E_{B}-E_{A}\end{array} \)

\(\begin{array}{l}=\frac{1}{4\pi \epsilon _{0}}\frac{q}{(r-a)^2}-\frac{q}{(r+a)^2}\end{array} \)

Simplifying the above equation, we get

\(\begin{array}{l}E_{p}=\frac{q}{4\pi \epsilon _{0}}\times \frac{2r}{(r^2-a^2)^2}\end{array} \)

Further simplifying, we get

\(\begin{array}{l}E_{p}=\frac{2kpr}{(r^2-a^2)^2}\end{array} \)

In the equation, p = 2aq and

\(\begin{array}{l}k = \frac{1}{4\pi \epsilon _{0}}\end{array} \)

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Frequently Asked Questions – FAQs

What is an electric dipole?

An electric dipole is defined as a pair of opposite charges q and –q separated by a distance d.

Is electric field intensity a scalar or vector quantity?

Electric field intensity is a vector quantity.

What is electric field?

The space around an electric charge in which its influence can be felt is known as the electric field.

What is electric field intensity?

The electric field intensity at a point is the force experienced by a unit positive charge placed at that point.

State true or false: The electric field intensity due to a positive charge is always directed away from the charge.

True.

The test charge used to measure the electric field intensity at a point should be infinitesimally small. Why?

The test charge used must be infinitesimally small so that it will not produce a field of its own. The actual value of the electric field intensity will get altered because of the field produced by the test charge.

Give an example of the electric dipole.

A pair of electric charges of two opposite signs and equal magnitude separated by a distance.

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Electric Field Intensity at any point due to an Ideal Dipole