The magnetic force (Vector FM)on a particle in a magnetic field is found by Vector FM = Vector I × Vector B, Vector I is the charge multiplied by the velocity of a charged particle and Vector B the strength of the magnetic field, in Tesla (T). An electron accelerates from rest to the right, in a horizontally directed electric field. The electron then leaves the electric field at a speed of 4.0 × 106, entering a magnetic field of magnitude 0.20 T (Tesla) directed into the screen. Calculate the magnitude and direction of the magnetic force on the electron. (Charge on an electron: q = 1.6 × 10-19)

Question

The magnetic force (Vector FM)on a particle in a magnetic field is found by Vector FM = Vector I × Vector B, Vector I is the charge multiplied by the velocity of a charged particle and Vector B the strength of the magnetic field, in Tesla (T). An electron accelerates from rest to the right, in a horizontally directed electric field. The electron then leaves the electric field at a speed of 4.0 × 106, entering a magnetic field of magnitude 0.20 T (Tesla) directed into the screen. Calculate the magnitude and direction of the magnetic force on the electron. (Charge on an electron: q = 1.6 × 10-19)

With full solutions?

Answer 1

To calculate the magnitude and direction of the magnetic force on the electron, we need to follow these steps:

Step 1: Calculate the charge multiplied by the velocity of the electron (Vector I).
Given:
Charge on an electron (q) = 1.6 × 10^-19 C (coulombs)
Velocity of the electron (v) = 4.0 × 10^6 m/s (meters per second)

Vector I = q * v

Substituting the values:
Vector I = (1.6 × 10^-19 C) * (4.0 × 10^6 m/s)
Vector I = 6.4 × 10^-13 C m/s

Step 2: Determine the direction of Vector I.
Since the electron is moving to the right, the direction of Vector I is taken as positive (+).

Step 3: Calculate the magnitude and direction of the magnetic force (Vector FM) using the equation Vector FM = Vector I × Vector B.

Magnitude of Vector FM = I * B (using magnitudes only)
Direction of Vector FM = Right-hand rule

Substituting the values:
Magnitude of Vector FM = (6.4 × 10^-13 C m/s) * (0.20 T)
Magnitude of Vector FM = 1.28 × 10^-13 N

Step 4: Determine the direction of Vector FM using the right-hand rule.
Using the right-hand rule:
- Point your fingers in the direction of the velocity of the charged particle (to the right).
- Curl your fingers to the direction of the magnetic field (into the screen).
- Your thumb will point in the direction of the magnetic force (out of the screen).

Therefore, the direction of Vector FM is out of the screen.

The final answer is:
Magnitude of the magnetic force (Vector FM) = 1.28 × 10^-13 N
Direction of the magnetic force (Vector FM) = Out of the screen.