An electron is ejected from the surface of a long, thick straight conductor carrying a current, initially in a direction perpendicular to the conductor. The electron will

Options

A. ultimately return to the conductor
B. move in a circular path around the conductor
C. gradually move away from the conductor along a spiral
D. move in a helical path, with the conductor as the axis

Explanation

To solve the problem of an electron ejected from a long, thick straight conductor carrying a current, we can follow these steps:

### Step 1: Understand the Situation
The problem states that an electron is ejected from the surface of a long, thick straight conductor that carries a current. The initial direction of the electron's velocity is perpendicular to the direction of the current.

**Hint:** Visualize the setup: draw the conductor, the direction of the current, and the initial velocity of the electron.

### Step 2: Determine the Direction of the Magnetic Field
Using the right-hand rule, we can determine the direction of the magnetic field (B) around the conductor. For a straight conductor carrying current, the magnetic field circles around the conductor.

- If the current is flowing upwards (for example), the magnetic field will be directed in a circular manner around the conductor. At the location of the electron, the magnetic field will be directed into the page (or screen).

**Hint:** Remember the right-hand rule: point your thumb in the direction of the current and curl your fingers around the conductor to find the direction of the magnetic field.

### Step 3: Calculate the Force on the Electron
The force (F) on the electron due to the magnetic field can be calculated using the formula:
\[ F = e \cdot (v \times B) \]
where:
- \( e \) is the charge of the electron,
- \( v \) is the velocity of the electron,
- \( B \) is the magnetic field.

Since the electron is negatively charged, the direction of the force will be opposite to the direction given by the right-hand rule.

**Hint:** Use the cross product to determine the direction of the force. Remember that the force on a negative charge is opposite to that calculated for a positive charge.

### Step 4: Analyze the Motion of the Electron
Initially, the electron is moving perpendicular to the current and experiences a magnetic force. This force will cause the electron to move in a curved path (like a projectile) due to the magnetic field acting on it.

**Hint:** Think about how the force changes the direction of the electron's velocity, resulting in circular or curved motion.

### Step 5: Conclusion
As the electron moves under the influence of the magnetic field, it will follow a curved trajectory and eventually return back to the conductor after traveling in a curved path.

**Hint:** Consider the nature of motion in a magnetic field and how charged particles behave under such conditions.

### Final Answer
The electron will return to the conductor after traveling in a curved path.