Askiitians Tutor Team
Last Activity: 4 Months ago
To find the average force on each electron in a coil carrying current placed in a magnetic field, we can use the principles of electromagnetism. The force experienced by a charged particle in a magnetic field can be calculated using the formula:
Understanding the Force on Electrons
The force \( F \) on a charged particle moving in a magnetic field is given by the equation:
F = q(v × B)
Where:
- F is the force on the charge (in Newtons)
- q is the charge of the particle (in Coulombs)
- v is the velocity of the particle (in meters per second)
- B is the magnetic field strength (in Tesla)
Step-by-Step Calculation
1. **Determine the Charge of an Electron**: The charge of a single electron is approximately \( 1.6 \times 10^{-19} \) Coulombs.
2. **Calculate the Current Density**: The current density \( J \) can be calculated using the formula:
J = \frac{I}{A}
Where:
- I is the current (0.2 A)
- A is the cross-sectional area of the wire (5 x 10-6 m2)
Substituting the values:
J = \frac{0.2}{5 \times 10^{-6}} = 4 \times 10^{4} \, \text{A/m}^2
3. **Calculate the Drift Velocity**: The drift velocity \( v_d \) of the electrons can be calculated using the formula:
v_d = \frac{J}{n \cdot q}
Where:
- n is the density of electrons (1029 /m3)
Substituting the values:
v_d = \frac{4 \times 10^{4}}{10^{29} \cdot 1.6 \times 10^{-19}} \approx 2.5 \times 10^{-4} \, \text{m/s}
4. **Calculate the Force on Each Electron**: Now we can find the force on each electron using the magnetic field strength \( B = 2 \, \text{T} \):
F = q \cdot v_d \cdot B
Substituting the values:
F = (1.6 \times 10^{-19}) \cdot (2.5 \times 10^{-4}) \cdot (2) \approx 8 \times 10^{-23} \, \text{N}
Final Thoughts
The average force on each electron in the coil, when subjected to the specified current and magnetic field, is approximately \( 8 \times 10^{-23} \) Newtons. This force is quite small, which is typical for individual electrons, but it plays a crucial role in the overall behavior of the current in the coil.
