Using Ampere's Law in finding H (magnetic field intensity)

In summary, by applying Ampere's law to the conducting slabs with uniform current densities in opposite directions, we can find the magnetic field intensity at different z positions. This can be done by using the Biot-Savart Law and Ampere's Circuital Law in a rectangular loop. More guidance and examples can be found in the textbook.
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jadi929
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Homework Statement



Let the regions 0 < z < 0.3 m and 0.7 < z < 1.0 m be conducting slabs carrying uniform current densities of 10 A/m^2 in opposite directions. Find H (the magnetic field intensity) and different z positions.

Homework Equations



Biot-Sarvot Law: H = ∫ (I dL X r)/ (4∏R2)

Ampere's Circuital Law: ∫ HdL = I

The Attempt at a Solution



I am guessing we have to apply ampere's law to each slab, in a rectangular loop. The slabs extend infinetly in the y and x axes. But I got no clue on exactly how to apply this law :( Any help would be appreciated as this my first post here.

Thanks!
 

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  • #2
Good idea. Surely your textbook has examples of how to apply Ampere's law.
 

FAQ: Using Ampere's Law in finding H (magnetic field intensity)

What is Ampere's Law and how is it used in finding H (magnetic field intensity)?

Ampere's Law is a fundamental law in electromagnetism that relates the circulation of the magnetic field around a closed loop to the electric current passing through the loop. It can be written as ∮C H·dL = Ienc, where H is the magnetic field intensity, C is the closed loop, and Ienc is the enclosed electric current. This law is used to calculate the magnetic field intensity at a given point in space.

What are the assumptions made when using Ampere's Law in finding H (magnetic field intensity)?

The main assumptions made when using Ampere's Law are that the electric current is constant and that the magnetic field is constant along the closed loop. Additionally, the closed loop must be chosen in a way that the magnetic field can be easily calculated or is already known at every point along the loop.

What are the units of H (magnetic field intensity) in Ampere's Law?

The units of H in Ampere's Law are amperes per meter (A/m). This is because H is defined as the magnetic field intensity caused by an electric current, and electric current is measured in amperes (A) and distance is measured in meters (m).

How is Ampere's Law used in practical applications?

Ampere's Law is used in many practical applications, such as in the design of electromagnets, motors, and generators. It is also used in the field of magnetohydrodynamics, which studies the interaction between magnetic fields and electrically conducting fluids. Additionally, Ampere's Law is used in the calculation of magnetic fields in MRI machines and other medical devices.

What are the limitations of Ampere's Law in finding H (magnetic field intensity)?

Ampere's Law is only valid for steady-state currents and cannot be applied to situations where the current is changing over time. It also assumes that the magnetic field is constant along the closed loop, which may not always be the case. Additionally, Ampere's Law does not take into account the effects of magnetic materials, which can alter the magnetic field intensity. These limitations should be considered when using Ampere's Law in practical applications.

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