Moving Charges and Magnetism

Class 12 | Physics

Magnetic Field (B):

• Magnetic field is a region around a magnet or a moving charge where it exerts a force on another magnet or moving charge.
• Magnetic field lines are imaginary lines used to represent the direction and strength of the magnetic field.
• Magnetic field lines always form closed loops.

Magnetic Field Due to a Current:

• A current-carrying conductor produces a magnetic field around it.
• The strength of the magnetic field depends on the current’s magnitude and decreases with distance from the conductor.
• Ampere’s Circuital Law relates the closed loop integral of magnetic field to the enclosed current.

Magnetic Force on a Current-Carrying Conductor:

• When a current-carrying conductor is placed in a magnetic field, it experiences a force.
• The direction of the force is given by Fleming’s Left-Hand Rule.
• The magnitude of the force depends on the current, the length of the conductor, and the strength of the magnetic field.

Magnetic Field Due to a Circular Loop:

• A circular loop carrying current creates a magnetic field at its center.
• The direction of the magnetic field is perpendicular to the plane of the loop and follows the right-hand thumb rule.
• The strength of the magnetic field at the center of the loop increases with an increase in current or the number of turns.

Ampere’s Circuital Law:

• Ampere’s law relates the magnetic field along a closed loop to the total current passing through the loop.
• It states that the line integral of the magnetic field around a closed path is equal to μ₀ times the enclosed current.

Magnetic Properties of Materials:

• Materials are classified into three categories based on their magnetic properties: ferromagnetic, paramagnetic, and diamagnetic.
• Ferromagnetic materials can be strongly magnetized and retain their magnetization even after the removal of the external magnetic field.
• Paramagnetic materials become weakly magnetized in the presence of an external magnetic field.
• Diamagnetic materials are weakly repelled by a magnetic field.

Earth’s Magnetism:

• Earth acts like a giant magnet with a north magnetic pole and a south magnetic pole.
• The magnetic axis of the Earth is tilted with respect to its rotational axis.
• The region where the magnetic field is vertical is called the magnetic meridian.
• The angle between the magnetic meridian and geographical meridian is called the declination.

Magnetic Properties of Earth:

• The Earth’s magnetic field is not uniform and has both horizontal and vertical components.
• The intensity of the magnetic field varies at different locations on Earth’s surface.
• The magnetic field lines emerge from the south pole and re-enter at the north pole, forming closed loops.

Important formulae

Moving Charges Important Formulae

IMPORTANT PROBLEMS

Magnetic Fields due to Currents:

1. Calculate the magnetic field at a point 10 cm away from a wire carrying a current of 5 A.
2. Determine the force between two parallel wires, each carrying a current of 2 A, and separated by a distance of 3 cm.
3. Find the magnetic field at the center of a circular loop with a radius of 0.1 m carrying a current of 3 A.

Magnetic Force and Motion:

4. A wire carrying a current of 4 A is placed in a magnetic field of 0.5 T. Calculate the force acting on the wire if it is 2 m long and perpendicular to the magnetic field.
5. A 0.2 m long wire carrying a current of 10 A is placed in a magnetic field of 0.4 T. Determine the force experienced by the wire if it is at an angle of 30 degrees to the field.
6. Calculate the radius of the path followed by an electron moving at a speed of 2 x 10^6 m/s in a magnetic field of 0.5 T.

Magnetic Properties of Materials:

7. A material has a magnetic susceptibility of 0.003. Determine whether it is diamagnetic, paramagnetic, or ferromagnetic.
8. If a paramagnetic sample has a magnetic susceptibility of 0.02, what will be its relative permeability?
9. A ferromagnetic material has a relative permeability of 800. Calculate its magnetic susceptibility.

Ampere’s Circuital Law:

10. Use Ampere’s law to find the magnetic field inside a long solenoid carrying a current of 2 A per turn, with 1000 turns per meter.
11. Calculate the magnetic field inside a circular loop carrying a current of 6 A, of radius 0.05 m, using Ampere’s law.
12. Find the magnetic field at a distance of 5 cm from a long straight wire carrying a current of 8 A using Ampere’s law.

Earth’s Magnetism:

13. Determine the magnetic declination at a location where the magnetic field lines are inclined at 30 degrees to the horizontal.
14. If the magnetic field strength at a certain location on Earth’s surface is 50 μT and the inclination is 60 degrees, calculate the horizontal component of the Earth’s magnetic field.
15. Calculate the total magnetic field strength at the magnetic north pole of the Earth.

Magnetic Force on Moving Charges:

16. An electron moves with a velocity of 3 x 10^6 m/s perpendicular to a magnetic field of 0.2 T. Calculate the force acting on the electron.
17. Find the radius of the circular path of a proton moving at 5 x 10^5 m/s in a magnetic field of 0.3 T.
18. A beam of electrons with a current of 2 mA enters a magnetic field of 0.4 T. Calculate the radius of the circular path followed by the electrons.
19. Determine the speed of an alpha particle (charge = 2e) required to move in a circle of radius 0.1 m in a magnetic field of 0.6 T.
20. Two parallel wires, each carrying a current of 10 A, are placed 2 cm apart. Calculate the force of repulsion between them.

Key

I can provide answers for the problems I previously mentioned:

**Magnetic Fields due to Currents:**

1. B = (μ₀ * I) / (2π * r) = (4π x 10⁻⁷ T·m/A * 5 A) / (2π * 0.1 m) = 10⁻⁶ T

2. F = (μ₀ * I₁ * I₂) / (2π * d) = (4π x 10⁻⁷ T·m/A * 2 A * 2 A) / (2π * 0.03 m) = 4 x 10⁻⁵ N

3. B = (μ₀ * I) / (2 * R) = (4π x 10⁻⁷ T·m/A * 3 A) / (2 * 0.1 m) = 6 x 10⁻⁶ T

**Magnetic Force and Motion:**

4. F = I * L * B * sin(θ) = 4 A * 2 m * 0.5 T * sin(90°) = 4 N

5. F = I * L * B * sin(θ) = 10 A * 0.2 m * 0.4 T * sin(30°) = 4 N

6. Radius (r) = (mv) / (qB) = [(9.11 x 10⁻³¹ kg) * (2 x 10⁶ m/s)] / [(1.6 x 10⁻¹⁹ C) * (0.5 T)] ≈ 1.14 x 10⁻² m

**Magnetic Properties of Materials:**

7. Diamagnetic.

8. Relative Permeability (μᵣ) = 1 + χ = 1 + 0.02 = 1.02 (Dimensionless)

9. Magnetic Susceptibility (χ) = (μᵣ – 1) = (800 – 1) = 799 (Dimensionless)

**Ampere’s Circuital Law:**

10. B = μ₀ * n * I = (4π x 10⁻⁷ T·m/A * 1000 A/m) = 4 x 10⁻⁴ T

11. B = (μ₀ * I) / (2 * R) = (4π x 10⁻⁷ T·m/A * 6 A) / (2 * 0.05 m) = 0.76 T

12. B = (μ₀ * I) / (2π * r) = (4π x 10⁻⁷ T·m/A * 8 A) / (2π * 0.05 m) = 0.16 T

**Earth’s Magnetism:**

13. Magnetic Declination = 30 degrees

14. Horizontal Component (H) = B * cos(θ) = 50 μT * cos(60°) = 25 μT

15. Total Magnetic Field Strength at the Magnetic North Pole ≈ 85,000 nT (nanoTesla)

**Magnetic Force on Moving Charges:**

16. F = q * v * B = (1.6 x 10⁻¹⁹ C) * (3 x 10⁶ m/s) * (0.2 T) = 9.6 x 10⁻14 N

17. Radius (r) = (mv) / (qB) = [(1.67 x 10⁻²⁷ kg) * (5 x 10⁵ m/s)] / [(1.6 x 10⁻¹⁹ C) * (0.3 T)] ≈ 0.003 m or 3 mm

18. Radius (r) = (mv) / (qB) = [(9.11 x 10⁻³¹ kg) * (5 x 10⁵ m/s)] / [(1.6 x 10⁻¹⁹ C) * (0.4 T)] ≈ 0.007 m or 7 mm

19. Speed (v) = (qBr) / m = [(2e) * (0.6 T) * (0.1 m)] / (2 * 9.11 x 10⁻³¹ kg) ≈ 6.59 x 10⁶ m/s

20. F = (μ₀ * I₁ * I₂) / (2π * d) = (4π x 10⁻⁷ T·m/A * 10 A * 10 A) / (2π * 0.02 m) = 10⁻³ N

Please double-check these calculations as there may be rounding errors.