Angular Momentum Magnetic Dipole Moments

The angular momentum of a particle is given by: Where: - is the position vector - is the linear momentum vector Angular momentum will be zero when the position vector and the linear momentum vector are parallel or antiparallel (i.e., when the angle between them is either 0° or 180°), because the cross product of parallel or antiparallel vectors is zero. However, angular momentum will be non-zero when the angle between the position vector and linear momentum vector is 90° because the cross product will give a maximum value. Thus, the correct answer is (C) angle between position vector and linear momentum is 90°.

The azimuthal quantum number determines the shape of the orbital and the magnetic quantum number determines the orientation of the orbital. The value of ranges from to , so .

Step 1: Understanding the Concept:
The magnetic moment ( ) of a bar magnet is the product of its pole strength ( ) and its magnetic length ( ).
Step 2: Key Formula or Approach:

When a magnet is cut, we must determine how its pole strength and length change.
Step 3: Detailed Explanation:
Let the initial magnetic moment be , where ' ' is the pole strength and ' ' is the total length.
When the magnet is cut into two equal halves perpendicularly (transversely to its magnetic axis):
- The pole strength ( ) remains completely unchanged because the cross-sectional area of the poles is not altered.
- The new length of each half becomes half of the original length, so .
Now, let's calculate the new magnetic moment ( ) for one of the halves:


Since the original magnetic moment was .
Substituting this back:

Step 4: Final Answer:
The magnetic moment of each half becomes half of the original value, .