The electron in the beam of a television tube move horizontally from south to north. The vertical component of the earth's magnetic field points down. The electron is deflected towards.

Options

A. west
B. no deflection
C. east
D. north to south

Answer

To solve the problem of the deflection of an electron in a magnetic field, we can follow these steps:

### Step 1: Identify the Direction of Electron Motion
The electron beam is moving horizontally from south to north. In terms of coordinate axes, we can consider:
- South to North as the positive y-direction.

### Step 2: Determine the Direction of the Magnetic Field
The problem states that the vertical component of the Earth's magnetic field points downwards. In terms of coordinate axes, we can represent:
- Downwards as the negative z-direction.

### Step 3: Use the Right-Hand Rule for Cross Product
The force acting on a charged particle moving in a magnetic field is given by the formula:
\[ \vec{F} = q (\vec{v} \times \vec{B}) \]
Where:
- \( q \) is the charge of the electron (negative).
- \( \vec{v} \) is the velocity vector of the electron.
- \( \vec{B} \) is the magnetic field vector.

### Step 4: Set Up the Vectors
From our previous steps:
- Velocity vector \( \vec{v} \) (electron moving from south to north) = \( +\hat{j} \) (positive y-direction).
- Magnetic field vector \( \vec{B} \) (pointing downwards) = \( -\hat{k} \) (negative z-direction).

### Step 5: Calculate the Cross Product
Now we calculate the cross product \( \vec{v} \times \vec{B} \):
\[ \vec{v} \times \vec{B} = \hat{j} \times (-\hat{k}) \]

Using the right-hand rule:
- Point your fingers in the direction of \( \hat{j} \) (upward).
- Curl them towards \( -\hat{k} \) (downward).
- Your thumb will point in the direction of the force.

The result of \( \hat{j} \times (-\hat{k}) \) is \( -\hat{i} \) (negative x-direction).

### Step 6: Interpret the Result
The negative x-direction corresponds to the west. Therefore, the electron will be deflected towards the west.

### Final Answer
The electron is deflected towards the **west**.

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