Question

If the magnetic field is along the positive y-axis and the electron is moving along the positive x-axis, the direction of force on the electron is

• A. along \(-y\) axis
• B. along \(+y\) axis
• C. along \(+z\) axis
• D. along \(-z\) axis

Hint:

Use \(\vec{F} = -e(\vec{v} \times \vec{B})\) for electrons and apply the right-hand rule.

Answer 1

The Correct Option is D

From Lorentz force law: \[ \vec{F} = q(\vec{v} \times \vec{B}) \] - \(\vec{v}\): along \(+\hat{x}\)
- \(\vec{B}\): along \(+\hat{y}\)
- \(q = -e\) (for electron)
Using the right-hand rule for \(\vec{v} \times \vec{B}\): \[ \vec{v} \times \vec{B} = \hat{x} \times \hat{y} = \hat{z} \Rightarrow \vec{F} = -e \cdot \hat{z} = -\hat{z} \] So the force is in the negative z-direction.

Answer 2

Step 1: Understand the problem
- Magnetic field, \(\mathbf{B}\), is along the positive y-axis: \(\mathbf{B} = +\hat{y}\)
- Electron velocity, \(\mathbf{v}\), is along the positive x-axis: \(\mathbf{v} = +\hat{x}\)
- Charge of electron, \(q = -e\) (negative charge)

Step 2: Use Lorentz force formula
The magnetic force on a moving charge is:
\[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \]

Step 3: Calculate the direction of \(\mathbf{v} \times \mathbf{B}\)
\[ \hat{x} \times \hat{y} = \hat{z} \]
Since the electron has negative charge, force direction is opposite:
\[ \mathbf{F} = -e \hat{z} = \text{along } -\hat{z} \text{ axis} \]

Step 4: Final answer
The force on the electron is along the \(-z\) axis.