An electron is moving northwards with a velocity `3*0xx10^7ms^-1` in a uniform magnetic field of `10T` directed eastwards. Find the magnitude and direction of the magnetic force on the electron. `(e=1*6xx10^(-19)C)`

Explanation

To find the magnitude and direction of the magnetic force on the electron, we can follow these steps:

### Step 1: Identify the given values
- Velocity of the electron, \( v = 3 \times 10^7 \, \text{m/s} \) (northward)
- Magnetic field strength, \( B = 10 \, \text{T} \) (eastward)
- Charge of the electron, \( q = -1.6 \times 10^{-19} \, \text{C} \)

### Step 2: Use the formula for magnetic force
The magnetic force \( F \) on a charged particle moving in a magnetic field is given by the equation:
\[ F = q \cdot v \cdot B \cdot \sin(\theta) \]
where:
- \( F \) is the magnetic force,
- \( q \) is the charge of the particle,
- \( v \) is the velocity of the particle,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.

### Step 3: Determine the angle \( \theta \)
Since the electron is moving northward and the magnetic field is directed eastward, the angle \( \theta \) between the velocity and the magnetic field is \( 90^\circ \). Thus, \( \sin(90^\circ) = 1 \).

### Step 4: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ F = (-1.6 \times 10^{-19} \, \text{C}) \cdot (3 \times 10^7 \, \text{m/s}) \cdot (10 \, \text{T}) \cdot \sin(90^\circ) \]
\[ F = (-1.6 \times 10^{-19}) \cdot (3 \times 10^7) \cdot (10) \cdot (1) \]

### Step 5: Calculate the magnitude of the force
Calculating the above expression:
\[ F = -4.8 \times 10^{-11} \, \text{N} \]
The negative sign indicates that the direction of the force is opposite to that of a positive charge.

### Step 6: Determine the direction of the force
To find the direction of the force, we can use the right-hand rule. For a positive charge, the force direction is given by the right-hand rule:
- Point your thumb in the direction of the velocity (north),
- Point your fingers in the direction of the magnetic field (east),
- Your palm will then face the direction of the force (upward).

Since the electron has a negative charge, the force will be in the opposite direction of the palm, which means it will be directed downward.

### Final Answer
- **Magnitude of the force**: \( 4.8 \times 10^{-11} \, \text{N} \)
- **Direction of the force**: Downward

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