Question

Two small magnets are placed along a straight line at a distance of 20 cm from each other and

their north poles are facing each other. If their magnetic moments be 0.2 J/T and 0.4 J/T, then

find the magnetic field at the middle point between them.​

Answer 1

Given:

Distance between the magnets = 20 cm

Magnetic moment of the first magnet(m₁) = 0.2 J/T

Magnetic moment of the second magnet(m₂) = 0.4 J/T

To find:

The magentic field at the mid point between them

Calculation:

The magnetic field at a point on the axis is given by the formula

       $B=\frac{\mu_{0}2M}{4\pi r^2}$

Calculate the magnetic field at point O due to magnet 1

       $B_{1}=\frac{\mu_{0}\times2\times0.4}{4\pi(10\times10^{-2})^2}$

Calculate the magnetic field at point O due to magnet 2

       $B_{2}=\frac{\mu_{0}\times2\times0.2}{4\pi(10\times10^{-2})^2}$

Resultant magnetic field (B) = B₁ - B₂

       $B= B_{1}-B_{2}$    

       $B=\frac{\mu_{0}\times2\times0.4}{4\pi(10\times10^{-2})^2}-\frac{\mu_{0}\times2\times0.2}{4\pi(10\times10^{-2})^2}$

       $B=\frac{2\mu_0}{4\pi (10\times10^{-2})^2} [0.4-0.2]$      

       $B=\frac{2\times10^{-7}}{10^{-2}} (0.2)$

       $B=4\times10^{-6}T$

Final answer:

The resultant magnet field at midpoint between them is 4×10⁻⁶ T and the direction of magnetic field is towards the magnet having magnetic moment of 0.2 J/T

       

           

             

     

Answer 2

Answer:

Two small magnets are placed along a straight line at a distance of 20 cm from each other and

their north poles are facing each other. If their magnetic moments be 0.2 J/T and 0.4 J/T, then

find the magnetic field at the middle point between them.