When a current in a circular loop is equivalently replaced by a magnetic dipole.

Options

A. the pole strength `m` of each pole is fixed
B. the distance `d` between the poles is fixed
C. the product `md` is fixed
D. none of the above

Answer

To solve the problem of when a current in a circular loop is equivalently replaced by a magnetic dipole, we can follow these steps:

### Step 1: Understand the Concept of Magnetic Dipole
A magnetic dipole is a magnetic entity that has a north and south pole, similar to a bar magnet. When a current flows through a circular loop, it generates a magnetic field that can be represented as a magnetic dipole.

### Step 2: Identify the Magnetic Dipole Moment
The magnetic dipole moment (μ) of a circular loop carrying current (I) can be expressed as:
\[ \mu = I \cdot A \]
where \( A \) is the area of the loop. For a circular loop of radius \( r \), the area \( A \) is given by:
\[ A = \pi r^2 \]
Thus, the magnetic dipole moment can be written as:
\[ \mu = I \cdot \pi r^2 \]

### Step 3: Determine the Magnetic Field Configuration
The magnetic field produced by a circular loop can be analyzed at different points. The magnetic field lines form closed loops, and the field is strongest at the center of the loop and diminishes as you move away from it.

### Step 4: Identify the Equatorial Position
The equatorial position of a magnetic dipole is the region where the magnetic field lines are parallel and the field strength is weaker than at the poles. For a magnetic dipole, the equatorial line is the line that bisects the dipole and is perpendicular to the axis of the dipole.

### Step 5: Relate the Circular Loop to the Magnetic Dipole
When we replace the current-carrying circular loop with an equivalent magnetic dipole, we can say that any point on the equatorial line of the dipole corresponds to a point on the circular loop. Thus, the point on the circular loop can be considered to be at a broadside-on position.

### Conclusion
In conclusion, when a current in a circular loop is replaced by a magnetic dipole, a point on the loop corresponds to the broadside-on position of the magnetic dipole.

### Answer
The answer to the question is option B (broadside on position).

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