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. X-axis
B. Y-axis
C. Z-axis
D. None of these

Answer

To solve the problem of a proton moving in a magnetic field, we can follow these steps:

### Step 1: Identify the Directions
- The proton is moving along the negative direction of the X-axis. This means its velocity vector \( \vec{v} \) can be represented as \( \vec{v} = -v \hat{i} \), where \( v \) is the speed of the proton.
- The magnetic field \( \vec{B} \) is directed along the positive direction of the Y-axis, represented as \( \vec{B} = B \hat{j} \).

### Step 2: Use the Lorentz Force Equation
- The Lorentz force \( \vec{F} \) acting on a charged particle moving in a magnetic field is given by the equation:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
where \( q \) is the charge of the proton. For a proton, \( q = +e \) (the elementary charge).

### Step 3: Calculate the Cross Product
- We need to calculate the cross product \( \vec{v} \times \vec{B} \):
\[ \vec{v} \times \vec{B} = (-v \hat{i}) \times (B \hat{j}) \]
- Using the right-hand rule and the properties of cross products, we find:
\[ \hat{i} \times \hat{j} = \hat{k} \]
- Therefore:
\[ \vec{v} \times \vec{B} = -vB (\hat{i} \times \hat{j}) = -vB \hat{k} \]

### Step 4: Determine the Direction of the Force
- Now substituting back into the Lorentz force equation:
\[ \vec{F} = q (-vB \hat{k}) = -e v B \hat{k} \]
- This indicates that the force \( \vec{F} \) is directed along the negative Z-axis (since \( \hat{k} \) represents the Z-axis).

### Conclusion
- 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.

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