Q.Two short bar magnets have magnetic moments 1.20 A m$^2$ and 1.00 A m$^2$ respectively. They are kept on a horizontal table parallel to each other with their north poles pointing towards south. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is (horizontal component of Earth's magnetic induction is $3.6\times10^{-5}$ Wb m$^{-2}$) (NSEP 2000-2001)

Step 1. Both magnets lie flat on the table with a common magnetic equator and north poles pointing the same relative way ("towards south"), so the midpoint O sits on the equatorial line of each magnet individually, at $r=10.0$ cm $=0.10$ m from each magnet's centre.

Step 2. Use the short-magnet equatorial field, $B_{eq}=\dfrac{\mu_0}{4\pi}\dfrac{p_m}{r^3}$, with $\mu_0/4\pi=10^{-7}$: for magnet 1 ($p_m=1.20$ A m$^2$), $B_1 = 10^{-7}\times1.20/(0.10)^3 = 10^{-7}\times1.20/0.001 = 1.2\times10^{-4}$ T.

Step 3. For magnet 2 ($p_m=1.00$ A m$^2$), $B_2 = 10^{-7}\times1.00/0.001 = 1.0\times10^{-4}$ T. …

Recognise the midpoint sits on the equatorial line of both magnets, then add the two equatori …

• Using the axial-line formula instead of the equatorial-line formula. …