How to Calculate Magnetic Field for Uniform Surface Current on XOY Plane?

In summary, the conversation discusses a problem with calculating the magnetic field at a specific point due to a uniform surface current. The attempted solution uses Stokes' theorem, but the answer does not match the given answer. The problem is caused by using a circle as the closed path, when a different shape is needed due to the direction of the magnetic field.
  • #1
mmainak
8
0

Homework Statement


am stuck on a magnetic field problem, please help me out..

The XOY plane carries a uniform surface current density k`=50 x^ A/m. What is the magnetic field at the point z = -0.5m?

Homework Equations



Curl B = mu0J

The Attempt at a Solution


using stokes theorem
Int[Curl B.ds`]=Int[B.dl`]= Int[mu0 J`.ds`]

B. 2.pi.(.5)=50.pi.(.5)^2

i.e B=25 wbbut the answer is given 10pi.10^-6 wb.
 
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  • #2
The problem with using a circle for the closed path integral is that B does not point "around the circle" for a surface current. So ∫B·dl is not simply B·circumference.

Instead, B will point along the same direction everywhere on one side of the surface. What shape does that suggest you should use as the closed path, for calculating ∫B·dl?
 

What is a magnetic field problem?

A magnetic field problem refers to any issue or challenge that arises when studying or working with magnetic fields. This can include understanding the behavior of magnetic fields, calculating their strength or direction, or manipulating them for practical applications.

How are magnetic fields created?

Magnetic fields are created by moving electric charges, such as electrons. The more charges are moving and the faster they are moving, the stronger the magnetic field will be.

What is the difference between a magnetic field and an electric field?

A magnetic field is created by moving electric charges, while an electric field is created by stationary electric charges. Magnetic fields can also interact with each other, while electric fields do not.

What are some real-world applications of magnetic fields?

Magnetic fields have a wide range of practical applications, including in generators and motors, magnetic resonance imaging (MRI) machines, compasses, and magnetic levitation trains.

How can I protect myself from the effects of magnetic fields?

While magnetic fields are generally not harmful to humans, exposure to very strong fields can have negative health effects. To protect yourself, limit your exposure to strong magnetic fields and use proper shielding when working with strong magnets.

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