In uniform magnetic field, if angle between `vec(v) and vec(B) is 0^(@) lt 0 lt 90^(@)`, the path of particle is helix. Let `v_(1)` be the component of `vec(v) along vec(B) and v_(2)` be the component perpendicular to `vec(B)`. Suppose p is the pitch. T is the time period and r is the radius of helix. Then
`T = (2pim)/(qB), r = (mv_(2))/(qB), P = (v_(1))T`
Assume a charged particle of charge q and mass m is released from the origin with velocity `vec(v) = v_(0) hat(i) - v_(0) hat(k)` in a uniform magnetic field `vec(B) = -B_(0) hat(k)`.
Axis of helix is along

Options

A. X-axis
B. Y-axis
C. Negative Y-axis
D. Z-axis

Explanation

To solve the problem, we need to analyze the motion of a charged particle in a uniform magnetic field. The key points to consider are the components of the velocity, the magnetic field direction, and the resulting path of the particle.

### Step-by-Step Solution:

1. **Identify the Components of Velocity**:
The velocity vector of the charged particle is given as:
\[ \vec{v} = v_0 \hat{i} - v_0 \hat{k} \]
We can break this down into components:
- The component along the magnetic field, \( v_1 \), is the component in the direction of \( \hat{k} \).
- The component perpendicular to the magnetic field, \( v_2 \), is the component in the direction of \( \hat{i} \).

Thus, we have:
\[ v_1 = -v_0 \quad \text{(along } \hat{k} \text{)} \]
\[ v_2 = v_0 \quad \text{(along } \hat{i} \text{)} \]

2. **Determine the Magnetic Field Direction**:
The magnetic field is given as:
\[ \vec{B} = -B_0 \hat{k} \]
This indicates that the magnetic field is directed along the negative \( z \)-axis.

3. **Identify the Axis of the Helix**:
Since the motion of the particle is helical, the axis of the helix will be aligned with the direction of the magnetic field. Given that the magnetic field is along the negative \( z \)-axis, the axis of the helix will also be along the \( z \)-axis.

4. **Conclusion**:
Therefore, the axis of the helix is along the direction of the magnetic field, which is:
\[ \text{Axis of helix is along } \hat{k} \text{ (z-axis)}. \]

### Final Answer:
The axis of the helix is along the \( \hat{k} \) direction (z-axis).

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