The magnetic field due to a short bar magnet | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The magnetic field $B$ on the axial line of a bar magnet at a distance $Z$ from its centre is given by the formula $B = \frac{\mu_0}{4 \pi} \frac{

Vedclass · Accepted Answer

$\frac{2 \mu_0}{4 \pi} \frac{M}{Z^3} \hat{M}$

Vedclass · Answer

(B) The magnetic field $B$ on the axial line of a bar magnet at a distance $Z$ from its centre is given by the formula $B = \frac{\mu_0}{4 \pi} \frac{2MZ}{(Z^2 - l^2)^2}$.For a short bar magnet,the length $2l$ is very small compared to the distance $Z$,i.e.,$Z \gg l$.Therefore,we can approximate $(Z^2 - l^2)^2 \approx (Z^2)^2 = Z^4$.Substituting this into the formula,we get $B = \frac{\mu_0}{4 \pi} \frac{2MZ}{Z^4} = \frac{\mu_0}{4 \pi} \frac{2M}{Z^3}$.In vector form,this is expressed as $\vec{B} = \frac{2 \mu_0}{4 \pi} \frac{\vec{M}}{Z^3}$.

The magnetic field due to a short bar magnet of magnetic dipole moment $M$ and length $2l$,on the axis at a distance $Z$ (where $Z \gg l$) from the centre of the magnet is given by . . . . . . .

Similar Questions

$A$ magnetic needle is kept in a non-uniform magnetic field. It experiences

Use:
$(i)$ the Ampere's law for $\vec{H}$ and
$(ii)$ continuity of lines of $\vec{B}$,to conclude that inside a bar magnet,
$(a)$ lines of $\vec{H}$ run from the $N$ pole to $S$ pole,while
$(b)$ lines of $\vec{B}$ must run from the $S$ pole to $N$ pole.

The average dipole moment of $Fe$ atoms is $1.8 \times 10^{-23} \ A-m^2$. The magnetic moment of an iron rod of length $10 \ cm$ and diameter $1 \ cm$ is........$A-m^2$: (density and atomic weight of $Fe$ are $7.87 \ g/cm^3$ and $55.87$ respectively).

$A$ sample of a ferromagnetic iron in the shape of a cube of side $1.0 \mu m$ contains $8.7 \times 10^{28}$ atoms per cubic metre and the magnetic dipole moment of each iron atom is $9.3 \times 10^{-24} A m^2$. Then the maximum possible magnetic dipole moment (in $A m^2$) of the sample is nearly

The magnetic field lines of a bar magnet

Vedclass Test Series

Exam Paper Generator

Online Exam Module