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)

Answer 1

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

Step 1: Calculate the charge-momentum vector (Vector I):
The charge-momentum vector, Vector I, is equal to the charge (q) multiplied by the velocity (v) of the electron. The charge of an electron is given as q = 1.6 × 10^-19 C (Coulombs) and the velocity of the electron is 4.0 × 10^6 m/s in this case. So, Vector I = (1.6 × 10^-19 C) × (4.0 × 10^6 m/s).

Step 2: Calculate the magnetic force vector (Vector FM):
The magnetic force vector, Vector FM, can be calculated using the cross product of Vector I and Vector B. Since Vector I and Vector B are perpendicular to each other (one is horizontal and the other is directed into the screen), the magnitude of the cross product simplifies to FM = |I| × |B|, where |I| is the magnitude of Vector I and |B| is the magnitude of Vector B.

Step 3: Calculate the magnitude and direction of the magnetic force:
Magnitude of Vector I (|I|) can be calculated using the charge-momentum vector formula, |I| = qv.

Plugging in the given values:
|I| = (1.6 × 10^-19 C) × (4.0 × 10^6 m/s) = 6.4 × 10^-13 kg⋅m/s

Now, using the simplified formula for the magnitude of the magnetic force:
FM = |I| × |B| = (6.4 × 10^-13 kg⋅m/s) × (0.20 T) = 1.28 × 10^-13 N.

The magnitude of the magnetic force is 1.28 × 10^-13 Newtons.

As for the direction, we can use the right-hand rule to determine the direction of the force. If we point our right thumb in the direction of the charge's velocity (to the right), and our fingers in the direction of the magnetic field (into the screen), then the force will be directed outward from the palm of our hand. Therefore, the direction of the magnetic force on the electron is out of the screen, perpendicular to both Vector I and Vector B.