An electron is moving along the positive x-axis . If the unifrom magnetic field is applied parallel to the negative z-axis, then
A. The electron will experience magnetic force along positive y-axis
B. The electron will experience magnetic force along negative y-axis
C. The electron will continue to move along the positive x-axis
E. The electron will move along circular path in magnetic field
Choose the correct answer from the options given below:

Options

A. B and E only
B. A and E only
C. C and D only
D. B and D only

Answer

To solve the problem, we need to analyze the motion of an electron in a magnetic field. Let's break it down step by step.

### Step 1: Identify the Direction of Motion and Magnetic Field
The electron is moving along the positive 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 electron and \( \hat{i} \) is the unit vector in the x-direction.

The magnetic field is applied parallel to the negative z-axis, which can be represented as:
\[ \vec{B} = -B \hat{k} \]
where \( B \) is the magnitude of the magnetic field and \( \hat{k} \) is the unit vector in the z-direction.

### Step 2: Use the Right-Hand Rule to Determine the Magnetic Force
The magnetic force \( \vec{F} \) on a charged particle moving in a magnetic field is given by the equation:
\[ \vec{F} = q \vec{v} \times \vec{B} \]
For an electron, the charge \( q \) is negative, so:
\[ \vec{F} = -e (\vec{v} \times \vec{B}) \]
where \( e \) is the magnitude of the charge of the electron.

### Step 3: Calculate the Cross Product \( \vec{v} \times \vec{B} \)
Now we calculate the cross product:
\[ \vec{v} \times \vec{B} = (v \hat{i}) \times (-B \hat{k}) \]
Using the right-hand rule, we can determine the direction of the cross product:
- Point your fingers in the direction of \( \vec{v} \) (positive x-axis).
- Curl them towards \( \vec{B} \) (negative z-axis).

This gives us a direction along the positive y-axis. Therefore:
\[ \vec{v} \times \vec{B} = vB \hat{j} \]
where \( \hat{j} \) is the unit vector in the y-direction.

### Step 4: Determine the Direction of the Magnetic Force
Since the charge of the electron is negative, the magnetic force will be:
\[ \vec{F} = -e (vB \hat{j}) = -evB \hat{j} \]
This means the force is directed along the negative y-axis.

### Step 5: Analyze the Motion of the Electron
The magnetic force acts perpendicular to the velocity of the electron. This will cause the electron to move in a circular path due to the centripetal force provided by the magnetic force. Therefore, the electron will not continue to move in a straight line along the x-axis but will instead move in a circular path in the xy-plane.

### Conclusion
From the analysis, we can conclude:
- The electron will experience a magnetic force along the negative y-axis (Option B).
- The electron will move along a circular path in the magnetic field (Option D).

### Final Answer
The correct options are B and D.

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