A proton is moving along the negative direction of X-axis in a magnetic field directed along the positive direction of Y-axis. The proton will be deflected along the negative direction of

Options

A. (a) X-axis
B. (b) Y-axis
C. (c) Z-axis
D. (d) None of these

Answer

To solve the problem, we will use the right-hand rule and the concept of the magnetic force acting on a charged particle moving in a magnetic field. Here are the steps to find the direction in which the proton will be deflected:

### Step 1: Identify the Direction of Velocity and Magnetic Field
- The proton is moving along the negative direction of the X-axis. This can be represented as a velocity vector \( \vec{v} = -\hat{i} \).
- The magnetic field is directed along the positive direction of the Y-axis, which can be represented as \( \vec{B} = +\hat{j} \).

### Step 2: Use the Formula for Magnetic Force
- The magnetic force \( \vec{F} \) acting on a charged particle is given by the equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
where \( q \) is the charge of the particle.

### Step 3: Calculate the Cross Product
- Since the charge of a proton \( q \) is positive, we can focus on the cross product \( \vec{v} \times \vec{B} \).
- Substituting the vectors:
\[ \vec{F} = q (-\hat{i}) \times (+\hat{j}) \]
- Using the right-hand rule for the cross product:
- Point your fingers in the direction of \( \vec{v} \) (negative X-axis).
- Curl your fingers in the direction of \( \vec{B} \) (positive Y-axis).
- Your thumb will point in the direction of \( \vec{F} \).

### Step 4: Determine the Direction of the Force
- The result of the cross product \( -\hat{i} \times \hat{j} \) gives \( -\hat{k} \), which means the force \( \vec{F} \) is directed along the negative Z-axis.

### Step 5: Conclusion
- Therefore, the proton will be deflected along the negative direction of the Z-axis.

### Final Answer
The proton will be deflected along the negative direction of the Z-axis.

---