According to Biot-Savart's law, an electron moving with velocity produces a magnetic field B such that:

Options

A. B is parallel to v
B. B is perpendicular to v
C. It obeys inverse cube law
D. H is along the line joining the electron and point of observation

Explanation

To solve the question regarding the magnetic field produced by an electron moving with a velocity according to Biot-Savart's law, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Biot-Savart's Law**:
Biot-Savart's law states that the magnetic field \( \mathbf{B} \) produced at a point in space by a moving charge \( Q \) is given by:
\[ \mathbf{B} = \frac{\mu_0}{4\pi} \frac{Q \mathbf{V} \times \hat{\mathbf{r}}}{r^2} \]
where \( \mathbf{V} \) is the velocity of the charge, \( \hat{\mathbf{r}} \) is the unit vector pointing from the charge to the point where the magnetic field is being calculated, and \( r \) is the distance from the charge to that point.

2. **Identifying the Components**:
- The term \( \mathbf{V} \times \hat{\mathbf{r}} \) indicates that the magnetic field \( \mathbf{B} \) is generated due to the cross product of the velocity vector and the position vector.
- The direction of the magnetic field is given by the right-hand rule applied to the cross product.

3. **Direction of Magnetic Field**:
- Since \( \mathbf{B} \) is produced by the cross product \( \mathbf{V} \times \hat{\mathbf{r}} \), it is perpendicular to both \( \mathbf{V} \) and \( \hat{\mathbf{r}} \). This means that the magnetic field \( \mathbf{B} \) is always perpendicular to the direction of the velocity \( \mathbf{V} \).

4. **Analyzing the Options**:
- If we analyze the options provided in the question:
- Option 1: \( \mathbf{V} \) is parallel to \( \mathbf{B} \) - This is incorrect since \( \mathbf{B} \) is perpendicular to \( \mathbf{V} \).
- Option 2: \( \mathbf{B} \) is perpendicular to \( \mathbf{V} \) - This is correct.
- Option 3: The magnetic field follows an inverse square law - This is also correct for the magnitude of the field, but the question focuses on the direction.
- Option 4: The magnetic field is along the line joining the charge and the point - This is incorrect as \( \mathbf{B} \) is not along this line.

5. **Conclusion**:
- The correct statement according to Biot-Savart's law is that the magnetic field \( \mathbf{B} \) produced by a moving charge is perpendicular to the velocity \( \mathbf{V} \).

### Final Answer:
The correct conclusion is that according to Biot-Savart's law, the magnetic field \( \mathbf{B} \) produced by an electron moving with velocity \( \mathbf{V} \) is perpendicular to \( \mathbf{V} \).