Biot-Savart law indicates that the moving electrons (velocity `vecv` ) produce a magnetic field `vecB` such that

Options

A. a. B is perpendicular to v
B. b. B is parallel to v
C. c. it obeys inverse cube law
D. D. it is along the line joining the electron and point of observation

Answer

To solve the question regarding the Biot-Savart law and the relationship between the velocity of moving electrons and the magnetic field they produce, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Biot-Savart Law**:
The Biot-Savart law states that the magnetic field \( \vec{B} \) produced at a point in space by a moving charge is directly related to the velocity \( \vec{v} \) of the charge and the position vector \( \vec{r} \) from the charge to the point of observation.

2. **Mathematical Expression**:
The mathematical expression for the Biot-Savart law is given by:
\[ \vec{B} = \frac{\mu_0}{4\pi} \frac{Q \vec{v} \times \vec{r}}{r^3} \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( Q \) is the charge of the moving electron,
- \( \vec{v} \) is the velocity vector of the electron,
- \( \vec{r} \) is the position vector from the charge to the point of observation,
- \( r \) is the magnitude of \( \vec{r} \).

3. **Direction of Magnetic Field**:
From the cross product \( \vec{v} \times \vec{r} \), we can determine the direction of the magnetic field \( \vec{B} \). The result of a cross product is always perpendicular to the plane formed by the two vectors. Therefore, \( \vec{B} \) is perpendicular to both \( \vec{v} \) and \( \vec{r} \).

4. **Analyzing the Options**:
- **Option A**: \( \vec{B} \) is perpendicular to \( \vec{v} \) - This is correct because \( \vec{B} \) is derived from the cross product of \( \vec{v} \) and \( \vec{r} \).
- **Option B**: \( \vec{B} \) is parallel to \( \vec{v} \) - This is incorrect as established above.
- **Option C**: It obeys the inverse cube law - This is incorrect; the magnetic field behaves according to the inverse square law in this context.
- **Option D**: It is along the line joining the electron and the point of observation - This is also incorrect; \( \vec{B} \) is not along this line.

5. **Conclusion**:
Based on the analysis, the correct answer is **Option A**: \( \vec{B} \) is perpendicular to \( \vec{v} \).