Question

Consider a bar magnet having pole strength 2 A-m magnetic length 4cm and area of cross section 1 cm^2 Find.



1. the magnetic intensity at the centre of magnet



2. magnetic field at the centre of magnet

Answer 1

The magnetic intensity at the centre of the magnet is $\frac{1}{4\pi } \text{x}10^{4}$ along the South Pole

Magnetic Field at the centre of the magnet $2.4 \text{x}10^{-2} \text{T}$ along with North Pole

Explanation:

Given :

Pole strength (m) = 2 A- m

Magnetic length =2l = 4 cm = $4 \text{x}10^{-2} \text{m}$  ( l = $2 \text{x} 10 ^{-2}$ m)

A = 1 cm² = $1 \text{x} 10^{-4} \text{m}^{2}$

To Find :

a) The magnetic intensity at the centre of the magnet

At the centre.

$\text{H}_{N} =$  (μ₀\4π x m\l²)\ μ₀

       = $\frac{\text{m}}{4\pi\text{l}^2}$

Similarly $\text{H}_{\text{S}} = \frac{\text{m}}{4\pi\text{l}^2 }$

Total Intensity = $\text{H}_{\text{N}} + \text{H}_{\text{S}}$

                          = $\frac{2\text{m}}{4\pi \text{l}^2}$ = $\frac{\text{m}}{2\pi\text{l}^{2} }$

                          = $\frac{2}{2 \text{x} 3.14 \text{x} (2 \text{x} 10^{-2})^{2} }}$

                         = $\frac{1}{4 \pi \text{x}10^{-4} } = \frac{1}{4\pi } \text{x}10^{4}$ along the South Pole

b) Magnetic Field at the centre of the magnet:

Magnetic Field, B =  μ₀ ( H + I )

Magnetisation , I =  $\frac{\text{M}}{\text{V}}$

                           = $\frac{\text{m} \text{x} 2 \text{l}}{\text{A} \text{x} 2 \text{l}}$  

                         = $\frac{2 \text{x} 4 \text{x} 10^{-2} }{4 \text{x}10^{-2}\text{x}10^{-4}}$

                   I     = $2 \text{x} 10^{4}$

                      = ${4\pi \text{x} 10^{-7}( \frac{1}{4\pi }\text{x} 10^{4} + 2 \text{x}10^{4})$

                    =   $4 \pi \text{x} 10^{-7}(\frac{1}{4\pi } +2)$

                       = $4 \pi\text{x}10^{-3}(\frac{1 + 8\pi }{4\pi } )$

                      = $2.4 \text{x}10^{-2} \text{T}$ along with North Pole.

To Learn More....

1. The point on the magnet where the magnetic intensity is maximum​

https://brainly.in/question/8712944

2. Magnetism at the centre of a bar magnet is

A. minimum B. maximum C. zero D. minimum or maximum

https://brainly.in/question/295924