뒤로Electromagnetism: Magnetic Fields, Circuits, and Current
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Magnetic Fields and Units
SI Units of Magnetic Field
The magnetic field, denoted as B, is a fundamental quantity in electromagnetism. Its SI unit is the tesla (T), which can be expressed in basic SI units as:
Unit of B:
Magnetic Dipole Moment
The magnetic dipole moment is a vector quantity that characterizes the strength and orientation of a magnet or current loop.
Unit:
Superconductivity and Magnetic Materials
Superconductors
Superconductors are materials that, below a certain critical temperature, undergo a phase transition and lose all electrical resistance. They also expel magnetic fields (Meissner effect).
Superconducting state: Zero resistance, expulsion of magnetic fields.
Ferromagnetic and Diamagnetic Materials
Copper (Cu): Diamagnetic (repels magnetic fields).
Nickel (Ni): Ferromagnetic (strongly attracted to magnetic fields).
Ferromagnetic materials have a high relative permeability (typically between 0.99 and 1.01).
Kirchhoff's Laws and Electric Circuits
Kirchhoff's Loop Rule
Kirchhoff's loop rule states that the sum of all potential differences around a closed loop is zero:
This is a consequence of energy conservation in electrical circuits.
Current in a Closed Loop
The current through a closed loop is related to the circulation of the magnetic field around the loop:
This is a statement of Ampère's Law.
Conservative Fields and Potential
Conservative Nature of Electric Fields
The electric field is conservative if:
This applies to static electric fields (electrostatics).
Electric Potential
The electric potential is related to the electric field by:
Capacitors and RC Circuits
Capacitor Charging and Discharging
When a capacitor is charged or discharged in an RC circuit, the charge and current follow exponential laws.
Equation for RC circuit:
Time constant:
Current and Charge Relations
Current:
Magnetic Field Due to Currents
Magnetic Field Inside a Wire
The magnetic field inside a long straight wire carrying current is given by:
(for )
Where is the radius of the wire, is the distance from the center, and is the permeability of free space.
Magnetic Field Outside a Wire
(for )
Force Between Parallel Currents
Parallel wires carrying currents exert forces on each other:
Force per unit length:
Like currents attract; opposite currents repel.
Current Density
Definition and Direction
Current density is a vector quantity representing the flow of electric charge per unit area:
Current density is a vector; current is a scalar.
Summary Table: Magnetic Field Formulas
Situation | Formula | Notes |
|---|---|---|
Inside wire () | Linear with | |
Outside wire () | Decreases with | |
Between parallel wires | Attractive if currents are same direction |
Additional info:
Some questions refer to topics not yet covered (as noted in the original file).
Explanations have been expanded for clarity and completeness.
