What is the relationship between current and magnetic moment in a closed loop?

In summary, the conversation discusses the equations for calculating magnitude and number of turns, current, and area in relation to Ampere's Law. It also mentions methods for calculating bound and free currents using the closed loop integral with the loop dl.
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Homework Statement


##magnitude(\vec{M})=NIS/c## N is number of turns, I is current and S is the Area
##N/(unit length) =NS*cos\theta## along a mathematical line

Homework Equations


Ampere Law ##\int_C\vec{B}d\vec{l} = 4*\pi/c*I_{link}##

##I_{Bound} = c\int_C\vec{M}d\vec{l}##

##\int_C(\vec{B}-4\pi\vec{M})d\vec{l} = 4*\pi/c*I_{free}##


The Attempt at a Solution



##\vec{M} = NIS/c*cos\theta##

##I_{Bound} = c\int_C NIS/c*cos\theta d\vec{l}##
Help doing the Closed Loop integral with loop dl!

##\int_C(\vec{B}-4\pi\vec{M})d\vec{l} = 4*\pi/c*(I_{link}-I_{bound}) = 4*\pi/c*I_{free}##
 
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  • #2
##I_{free} = \int_C(\vec{B}-4\pi NIS/c*cos\theta)d\vec{l}##Help doing the Closed Loop integral with loop dl!
 

1. What is linked current in electricity?

Linked current, also known as mutual current, is the flow of electric charge between two or more circuits that are connected by a magnetic field. This can occur when two or more inductors are placed close together, causing the magnetic fields produced by each inductor to interact and induce a current in the other circuit.

2. How is linked current different from bound current?

Linked current refers to the flow of charge between two separate circuits, while bound current refers to the flow of charge within a single circuit. Bound current is caused by the magnetic field produced by the current flowing through the circuit itself, whereas linked current is caused by the interaction of magnetic fields between separate circuits.

3. What are some applications of linked and bound current?

Linked and bound current have various applications in electrical engineering, including in the design of transformers, motors, and generators. They are also important in the study of electromagnetic fields and their effects on electronic devices.

4. How is linked current related to Faraday's law of induction?

Linked current is a manifestation of Faraday's law of induction, which states that a changing magnetic field can induce an electric current in a nearby conductor. In the case of linked current, the changing magnetic fields of two separate circuits induce a current in each other.

5. How can linked and bound current be calculated?

Linked and bound current can be calculated using equations based on the principles of electromagnetism, such as Ampere's law and Faraday's law. These equations take into account factors such as the strength of the magnetic field, the number of turns in an inductor, and the rate of change of the magnetic field. Advanced mathematical techniques, such as vector calculus, may also be used to calculate these currents.

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