How Does Mass Affect the Magnetic Field Strength of a Bar Magnet?

[thatoneguy123]

A particular Alnico (aluminum, cobalt, nickel, and iron) bar magnet (magnet A) has a mass of 10 g. It produces a magnetic field of magnitude 3e-05 T at a location 0.19 m from the center of the magnet, on the axis of the magnet.

(a) Approximately what is the magnitude of the magnetic field of magnet A a distance of 0.57 m from the center of the magnet, along the same axis? answer is 1.11111e-5

(b) If you removed the original magnet, and replaced it with a magnet made of the same material, but with a mass of 40 g (magnet B), approximately what would be the magnetic field at a location 0.19 m from the center of the magnet, on the axis of the magnet?



i knwo that bar magnets are dipoles so i used the dipole equation and solved for mew and plugged in the new r and got 1.11111e-5 for a and that is correct but it know no clue how to do number too i thought it was be a 1/4 proportionality but it isn't anyone have any ideas?

 

[anathema]

For part (b), we can use the dipole equation again, but this time we will solve for the magnetic field (B) instead of the magnetic moment (mew). The equation is B = (mu0/4pi)*((2m)/(r^3)), where mu0 is the permeability of free space, m is the magnetic moment, and r is the distance from the center of the magnet.

Since we are told that magnet B has a mass of 40 g, we can assume that its magnetic moment is four times that of magnet A (since the mass is four times greater). Therefore, the magnetic moment of magnet B is 4*2.5e-5 = 1e-4 A*m^2.

Plugging this into the equation, along with the new distance of 0.19 m, we get: B = (4*pi*1e-7)*((2*1e-4)/(0.19^3)) = 1.778e-5 T.

So, the magnetic field at a distance of 0.19 m from the center of magnet B would be approximately 1.778e-5 T.