Ampere's law -- application with two conducting loops

In summary, the conversation discusses using Amperes law to determine the direction of current and the confusion that arises when assigning the direction for different integration points. The speaker suggests drawing a picture of the system to better understand the direction of current.
  • #1
Physicslearner500039
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Homework Statement
Figure 29-67 shows two closed paths wrapped around two conducting loops carrying currents
i j = 5.0 A and i2 = 3.0 A. What is the value of the integral ~ B· d'S for (a) path 1 and (b) path2?
Relevant Equations
No specific equations
I am trying to get more confidence on the direction of current using Amperes law, the problem statement is
Amp3.JPG

Loop1:
My first task was to assign the direction of current. If I wrap around the my right hand fingers in the direction of integration the thumb is pointing up hence Positive Y direction current is +Ve and Negative Y direction current is -Ve. Hence i1 is -ve and i2 is +Ve.
∫B.ds = (-5+3)*μ = -2*4*π*10^-7 = -2.5u T.m.
Is everything ok?

Loop2:
The real confusion happens here while assigning the current direction I have shown the integration points
Amp3_2.JPG

Right hand rules for integration points
A: Up current is positive.
B: Up current is negative.
C: Up current is positive.
So which direction should i consider positive?
For side 1 the current is one direction and for side 2 it is opposite direction. Do they always cancel? Please advise.
 
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  • #2
I suggest that you draw a picture of the system as seen from above, including the currents going in/out of the paper and the loop with directional arrows.
 
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FAQ: Ampere's law -- application with two conducting loops

What is Ampere's law?

Ampere's law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. It states that the integral of the magnetic field around a closed loop is equal to the current passing through the loop multiplied by a constant known as the permeability of free space.

How is Ampere's law applied with two conducting loops?

With two conducting loops, Ampere's law can be used to calculate the magnetic field at a point due to the current passing through both loops. This can be done by taking the integral of the magnetic field around a closed path that encloses both loops.

What are some real-world applications of Ampere's law with two conducting loops?

Ampere's law with two conducting loops is used in many practical applications, such as in the design of electromagnetic devices like electric motors and generators. It is also used in the study of magnetic fields and their effects on charged particles in particle accelerators and fusion reactors.

How does the orientation of the two conducting loops affect the application of Ampere's law?

The orientation of the two conducting loops can affect the application of Ampere's law, as it determines the direction and magnitude of the magnetic field at a given point. The relative position and orientation of the loops must be taken into account when using Ampere's law to calculate the magnetic field.

Are there any limitations to the application of Ampere's law with two conducting loops?

While Ampere's law is a useful tool for calculating magnetic fields, it has limitations when applied to more complex systems. For example, it assumes that the current passing through the loops is constant and does not take into account magnetic materials or time-varying currents. In these cases, other laws and equations must be used in conjunction with Ampere's law to accurately describe the magnetic field.

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