A point charge is moving in clockwise direction in a circle with constant speed. Consider the magnetic field produced by the charge at a fiexed point P (not at the centre of circle ) on the axis of the circle. Then,

Options

A. it is constant in magnitude only
B. it is a constant in direction only
C. it is constant in direction and magnitude and magnitude both
D. it is not constant in magnitude and direction both

Answer

To solve the problem of determining the magnetic field produced by a point charge moving in a circle at a fixed point P on the axis of the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Motion of the Charge**:
- A point charge \( q \) is moving in a circular path with constant speed \( v \). This circular motion implies that the charge is continuously changing its direction, which is essential for generating a magnetic field.

2. **Magnetic Field Due to a Moving Charge**:
- The magnetic field \( \vec{B} \) created by a moving charge can be calculated using the Biot-Savart Law. For a point charge moving with velocity \( \vec{v} \), the magnetic field at a point in space is given by:
\[ \vec{B} = \frac{\mu_0}{4\pi} \cdot \frac{q \cdot \vec{v} \times \hat{r}}{r^2} \]
where \( \hat{r} \) is the unit vector pointing from the charge to the point where the magnetic field is being measured, and \( r \) is the distance from the charge to that point.

3. **Analyzing the Magnetic Field at Point P**:
- Since the charge is moving in a circle, at any instant, it will create a magnetic field at point P. The direction of the magnetic field will depend on the direction of the velocity of the charge and the position of point P relative to the charge.

4. **Magnitude of the Magnetic Field**:
- As the charge moves in a circular path, the distance from the charge to point P remains constant. Thus, the magnitude of the magnetic field at point P will also remain constant as the charge moves around the circle.

5. **Conclusion**:
- Since the charge is moving with constant speed in a circular path, and the distance to point P does not change, the magnetic field at point P is constant in magnitude. However, the direction of the magnetic field may change as the charge moves, but the magnitude remains the same.

### Final Answer:
The magnetic field produced by the charge at point P is constant in magnitude only.

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