Electric field due to a dipole at a equatorial point depends upon r-n . Value of n is
Approach Solution - 1
The correct answer is : 3
At an equatorial point of a dipole, the electric field due to the dipole is given by:
\(E = k [\frac{p}{ (r^3)}]\)
where k is the Coulomb constant, p is the dipole moment, and r is the distance from the dipole.
For an equatorial point, the distance r is equal to the distance between the two charges of the dipole, which is 2a, where a is the separation between the charges.
Therefore, the electric field at the equatorial point can be written as:
\(E = k [\frac{p}{ (2a)^3}]\)
\(E = (\frac{1}{4πε0}) [\frac{2psinθ}{ (2a)^3}]\)
where θ is the angle between the axis of the dipole and the line joining the dipole to the point where the electric field is to be calculated, and ε0 is the permittivity of free space.
Since sinθ = 1 at the equatorial point, we can simplify the above equation as:
\(E = (\frac{1}{4πε0)} [\frac{psinθ}{ a^3}]\)
\(E = (\frac{1}{4πε0}) [\frac{p}{ a^3}]\)
Therefore, the dependence of the electric field on the distance r at an equatorial point is \(\frac{1}{r^3}\), which is equivalent to n = 3.
Hence, the value of n is 3.
Approach Solution -2
The correct answer is : 3
\(\vec{E}=\frac{KP}{r^3}\)
\(⇒E∝\frac{1}{r^3}\)
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Concepts Used:
Electric charges and field
What is Electric Charge
It is the property of subatomic particles that experiences a force when put in an electric and magnetic field.
What is Electric Field
It is a property associated with each point in space when charge is present in any form. The magnitude and direction of the electric field are expressed by E, called electric field strength or electric field intensity.
Electric charges are of two types: Positive and Negative. It is commonly carried by charge carriers protons and electrons.
Properties of Electric Charge
Various properties of charge include the following :-
- Additivity of Electric Charge
- Conservation of Electric Charge
- Quantization of Electric Charge
Types of electric charge
Two kinds of electric charges are there :-
Negative Charge - When an object has a negative charge it means that it has more electrons than protons.
Positive Charge - When an object has a positive charge it means that it has more protons than electrons.
When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.