1 Part A A typical experiment is as follows: Go outside, at least several meters away from buildings, and face north (use a compass). Align your magnet as shown, with

the south pole of the compass facing north. How do you know which side is the south pole? Since Bm points towards the south pole of magnets, and the Earth's field points towards the geographic North Pole, if you move your compass towards and away from the mag-net, there should be a “null point" along the axis of the magnet where the magnetic fields due to the Earth and magnet cancel. The compass will flip directions around this point (if the compass never “flips", then you have your magnet oriented backwards). Measure the distance from the null point to the center of your magnet(this will be our distance r).Now BE and Bm are oppositely directed, and since it's a null point, their vector sum must be 0. Take the Earth's field BE = 2 × 10^-5 T (or 0.2 Gauss),and since the magnet generates a dipole field that (in magnitude) is equivalent to that from a distant current-carrying coil, \overrightarrow{\boldsymbol{B}}_{\boldsymbol{z}}+\overrightarrow{\boldsymbol{B}}_{\boldsymbol{m}}=\mathbf{0} B_{B}=B_{m}=\frac{\mu_{9}}{4 \pi} \frac{2 \mu}{r^{3}} 1._______If the null point is r = 27 cm, find µ, the magnetic dipole moment of the magnet. 2.___________ Remember that since a permanent magnet's field is equivalent to that from a current loop, and µ = IA, find the I for a loop you'd need to produce a B-field equivalent to the magnet(suppose the current loop would have r = l cm). Yes, it's a lot of current– these are strong magnets! 3._________Now that you know µ, find the Bm strength (in Tesla) close (r = 1 cm) to the magnet. 2 Part B Now we turn the magnet 90° as shown, so the north pole of the magnet faces east. Note the directions of the magnet's field Bm and the Earth BẸ. 1._______At some distance r the compass deflection from north is 6 = 60°. Find Bm at this r using the geometry of the system, the known value of Be, and a trig function (do not use the u you calculated in A). 2.________Now we double the distance to 2r and carefully measure the new compass deflection from north (this is a more delicate measurement). Suppose this deflection is now about 12°. Again, using trigonometry, calculate the Bm at this new distance from your average deflection. 3.________By what factor (very roughly) did Bm decrease when r doubled? In other words, did it go down by a factor of 4, 8, 10... ? 4.___________If the magnetic field strength decreases as , by what factor should the field strength de-crease? Is this consistent with what what found?