A proton is moving along `Z`-axis in a magnetic field. The magnetic field is along `X`-axis. The proton will experience a force along

Options

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

Answer

To solve the problem, we need to determine the direction of the force experienced by a proton moving along the Z-axis in a magnetic field that is directed along the X-axis. We can use the right-hand rule and the formula for the magnetic force on a charged particle.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The proton is moving along the Z-axis.
- The magnetic field is directed along the X-axis.

2. **Define the Vectors:**
- Let the velocity vector of the proton be represented as \( \vec{v} = v \hat{k} \) (where \( \hat{k} \) is the unit vector in the Z-direction).
- Let the magnetic field vector be represented as \( \vec{B} = B \hat{i} \) (where \( \hat{i} \) is the unit vector in the X-direction).

3. **Use the Formula for Magnetic Force:**
- The magnetic force \( \vec{F} \) experienced by a charged particle is given by the equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
- Here, \( q \) is the charge of the proton (which is positive).

4. **Calculate the Cross Product:**
- We need to calculate \( \vec{v} \times \vec{B} \):
\[ \vec{v} \times \vec{B} = (v \hat{k}) \times (B \hat{i}) \]
- Using the right-hand rule for the cross product:
- Point your fingers in the direction of \( \hat{k} \) (Z-axis).
- Curl them towards \( \hat{i} \) (X-axis).
- Your thumb will point in the direction of the resultant vector, which is \( \hat{j} \) (Y-axis).

5. **Determine the Direction of the Force:**
- Since the charge \( q \) is positive (for a proton), the direction of the force \( \vec{F} \) will be in the same direction as \( \vec{v} \times \vec{B} \).
- Therefore, the force \( \vec{F} \) is directed along the Y-axis.

6. **Conclusion:**
- The proton will experience a force along the Y-axis.

### Final Answer:
The proton will experience a force along the Y-axis.

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