You are hiking through the Joshua Tree National Monument in California when you

Question

You are hiking through the Joshua Tree National Monument in California when you find to your consternation that a small grain of sand has become lodged in your compass. The pesky particle is right at the end of the compass needle, 2.15 cm from the needle's pivot point. Using a friend's compass to establish magnetic north, you hold your compass with its needle perpendicular to this direction, reasoning that the Earth's magnetic field of 5.00×105 T will apply maximum torque to it in this orientation. You tap on the compass, hoping to free up the needle. What force is the tip of the needle exerting on the grain of sand? Your compass needle has a magnetic dipole moment of 0.0188 J/T.

Explanation / Answer

Magnetic dipole moment () of the compass needle = 0.0188J/T We know the formula for the torque acting on the compassneedle due to the magnetic field is                          = B And also we have the general formula for the torque is = rF Equating these two formulae we get                 rF = B                  F = (B) / r                     = (0.0188 J/T)(5.00×105 T) /(2.15*10-2m) Do the calculation work ofr finding the value of the forceacting on the compass needle.

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