There was a problem in my book that read- A magnet is pointing towards geographic north at a place where the horizontal component of the Earth's magnetic field is 40 microtesla. Magnetic dipole moment of the bar is 60 Am^2 and the torque acting on it is 1.2 x 10^-3 Nm. What's the declination at this place? Now, the angle of declination is defined as the angle between the true geographic north-south direction and the north-south line shown by the compass needle. Since the magnet is pointing toward the geographic north shouldn't the angle of declination be zero? The solution of the problem involved equating torque with M x B which gave sin $\theta$ = 0.5 (where $\theta$ is the angle between the vectors M and B). Even if the angle of declination is not zero, how can we be sure that it is 30 degrees? Please explain this with a sketch.
$\begingroup$
$\endgroup$
2
asked Sep 2, 2020 at 4:13
-
$\begingroup$ the magnet is pointing toward the geographic north No, it is pointing towards magnetic north. See en.wikipedia.org/wiki/Geomagnetic_pole $\endgroup$– G. SmithCommented Sep 2, 2020 at 4:50
-
$\begingroup$ The problem states that the magnet is pointing toward the geographic north. $\endgroup$– R.W. BirdCommented Sep 2, 2020 at 16:46
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
2
In this case we have to assume that the support for magnet keeps it horizontal while allowing it to rotate around a vertical axis. Since it is not in line with the horizontal component of the earths field, there will be a torque acting on it of: τ = MBsin(θ) which is trying to bring it into alignment. The θ is the angle between the true north and the direction of the horizontal component of the field.
-
$\begingroup$ Thank you so much, I understand it better now. But then, what about the vertical component of the earth's field? And it's not just in this case, I have seen multiple instances when the vertical component is omitted, as though it doesn't exist at all! Could you tell me why it is so? $\endgroup$ Commented Sep 3, 2020 at 8:01
-
$\begingroup$ Concern about the vertical component of the field depends on what you are doing. A compass needle (like your magnet) responds to the horizontal component of the field. If you want to use a Helmholtz coil to cancel the earths field (within a limited volume), it has to be tipped to align with the field. $\endgroup$ Commented Sep 3, 2020 at 14:14