Magnetic Field Intensity of a Bar Magnet

Questions and Answers

What is a magnetic dipole composed of?

A pair of unequal poles

A pair of equal and opposite poles (correct)

A magnetic pole and a neutral point

A single magnetic pole

How is the magnitude of a magnetic dipole movement expressed mathematically?

$M = m / 2l$

$M = m.2l$ (correct)

$M = m + 2l$

$M = m - 2l$

What does the direction of magnetic dipole movement indicate?

In a circular direction around the dipole

From North Pole to South Pole

From South Pole to North Pole (correct)

At a right angle to the poles

What does the magnetic poles refer to in a bar magnet?

Regions near the ends of the magnet where the force is maximum Signup and view all the answers

What is represented by the vector quantity $oldsymbol{ ext{M}}$?

Magnetic dipole movement Signup and view all the answers

What does Coulomb's law indicate about the relationship between force and distance?

Force is inversely proportional to the distance between the poles. Signup and view all the answers

In Coulomb's law, the force of attraction or repulsion is proportional to what factors?

The product of the pole strengths and the square of the distance. Signup and view all the answers

What is the value of the proportionality constant $ u_0$ in Coulomb's law?

$10^{-7} rac{Tm}{A}$ Signup and view all the answers

What does the direction of the force between two magnetic poles depend on?

The line joining both poles. Signup and view all the answers

How is the overall equation for force $F$ in magnetism derived according to Coulomb's law?

$F = rac{ u_0}{4 heta} imes rac{m_1m_2}{d^2}$ Signup and view all the answers

What represents the magnetic field intensity at point P?

$rac{μ₀m}{4πr²}$ Signup and view all the answers

What does the symbol $μ₀$ represent?

Permeability of air or free space Signup and view all the answers

What is the expression for the magnetic field intensity at point P due to the positive magnetic moment +m?

$B_1= rac{ u_o}{4eta}rac{m}{(l-l)^2}ighat{i}$ Signup and view all the answers

Which of the following is true regarding the formula for force between two magnetic poles?

It is directly proportional to the product of the pole strengths Signup and view all the answers

What is the formula for the net magnetic field intensity at point P due to the bar magnet?

$B_{net} = rac{2 u_o}{eta} [ rac{M}{(l^2-l^2)^2}]ighat{i}$ Signup and view all the answers

How does the distance $r$ affect the magnetic field intensity at point P?

It is inversely proportional to the square of the distance Signup and view all the answers

When considering the magnetic field intensity contributions from both +m and -m, what is the correct evaluation for $B_1$ at point P?

$B_1 = rac{ u_o}{4eta}rac{m}{(l-l)^2}ighat{i}$ Signup and view all the answers

If $m_2$ is set to 1 in the formula, how does this affect the calculation of magnetic field intensity?

It does not change the calculations for magnetic field intensity Signup and view all the answers

What is the simplified form of the magnetic field expression for $B_{net}$ at point P?

$B_{net} = rac{2 u_o}{eta} [ rac{M}{(l^2 - l^2)^2}]ighat{i}$ Signup and view all the answers

What happens to the equation for the magnetic field intensity when the distance l approaches zero?

It results in an infinite magnetic field intensity. Signup and view all the answers

Study Notes

Magnetic Field Intensity at Axial Point of a Bar Magnet

A magnetic dipole is characterized by a dipole moment, represented as ( \vec{M} = m \cdot 2\ell \hat{i} ).
The magnetic field intensity at point P due to the positive pole (+m) is expressed as ( B_1 = \frac{\mu_0}{4\pi} \frac{m}{(l-l)^2} \hat{i} ).
The magnetic field intensity at point P due to the negative pole (-m) is given by ( B_2 = \frac{\mu_0}{4\pi} \frac{m}{(l+l)^2} \hat{i} ).
The net magnetic field intensity at point P is calculated as ( B_{net} = B_1 + B_2 ).
By simplifying the formula, the net magnetic field intensity can be expressed as ( B_{net} = \frac{2\mu_0}{\pi} \left[ \frac{M}{(l^2 - l^2)^2} \right] \hat{i} ).

Coulomb's Law in Magnetism

The force between two magnetic poles is proportional to the product of their strengths and inversely proportional to the square of the distance between them.
Formal expressions include:
- ( F \propto m_1 m_2 )
- ( F \propto \frac{1}{d^2} )
Combining these results gives the force formula:
- ( F = \frac{\mu_0}{4\pi} \cdot \frac{m_1 m_2}{d^2} )
The proportionality constant ( \mu_0 ) (permeability of free space) is approximately ( 10^{-7} , \text{Tm/A} ).

Magnetic Concepts

Magnetic Poles

Areas near the ends of a bar magnet where the magnetic force is most intense.

Magnetic Dipole

Formed by two equal and opposite magnetic poles in close proximity.

Magnetic Dipole Moment

Denotes the strength of a magnetic dipole, represented as ( \vec{M} ).
The formula for magnetic dipole moment is:
- ( M = m \cdot 2l )
Directionally, it extends from the South Pole to the North Pole.