Scalar magnetic potential

Scalar magnetic potential (Vm) is different from the electric potential in that the scalar magnetic potential is not a function of positions and there is no physical interpretation.

• Scalar magnetic potential (Vm) is different from the electric potential in that the scalar magnetic potential is not a function of positions and there is no physical interpretation.

• Vector magnetic potential (A) is useful to find a magnetic field for antenna and waveguide. We can transform Bio-Savart’s law and can show that

Magnetic force on a moving charge N.

• Magnetic force on a moving charge N.

• Magnetic force on a current element N.

• For a straight conductor in a uniform magnetic field or F = ILBsin N.

• Torque on a closed circuit in which current is uniform can be expressed as Nm.

• For current loop that has uniform current and magnetic field, torque can be expressed as

a)

• a)

b)

• b)

• c)

• d)

a)

• a)

• b)

c)

• c)

• d)

Flux linkage is the total flux passing through the surface bounded by the contour of the circuit carrying the current.

• Flux linkage is the total flux passing through the surface bounded by the contour of the circuit carrying the current.

• Inductane L is defined as the ratio of flux linkage to the current generating the flux,

• henrys or Wb/A.

1. Assume a current I in the conductor

• 1. Assume a current I in the conductor

• 2. Determine using the law of Bio-Savart, or Ampere’s circuital law if there is sufficient symmetry.

• 3. Calculate the total flux  linking all the loops.

• 4. Multiply the total flux by the number of loops to get the flux linkage.

• 5. Divide the flux linkage by I to get the inductance. The assumed current will be divided out.

The definition of the inductance can be written in the form of magnetic energy as

• The definition of the inductance can be written in the form of magnetic energy as

• The current inside conductor creates the magnetic flux inside the material texture. This flux causes an internal inductance which combines with the external inductance to get the total inductance. Normally, the internal inductance can be neglected due to its small value compared to the external one.

Mutual inductance M is the inductance that is caused by the flux linking to the different circuit. The mutual inductance between circuit 1 and circuit 2 can be expressed as

• Mutual inductance M is the inductance that is caused by the flux linking to the different circuit. The mutual inductance between circuit 1 and circuit 2 can be expressed as

a) A coaxial cable with the length l = 10 m, the inner radius a = 1 mm, and the outer radius b = 4 mm. The inserted magnetic material has r = 18 and r = 80.

• a) A coaxial cable with the length l = 10 m, the inner radius a = 1 mm, and the outer radius b = 4 mm. The inserted magnetic material has r = 18 and r = 80.

b) A toroid with a number of turns N = 5000 turns with in = 3 cm, out = 5 cm, and the length l = 1.5 cm. The inserted material has r = 6.

• b) A toroid with a number of turns N = 5000 turns with in = 3 cm, out = 5 cm, and the length l = 1.5 cm. The inserted material has r = 6.

• c) A solenoid has the radius r = 2 cm, the length l = 8 cm, and N = 900 turns. The inserted material has r = 100.

a) Given the current I = 1 A, determine H inside the solenoid when the inner solenoid is removed.

• a) Given the current I = 1 A, determine H inside the solenoid when the inner solenoid is removed.

b) Determine the resulting self inductance.

• b) Determine the resulting self inductance.

• c) Determine the mutual inductance between two solenoids.