How does the radial current density affect the area element dA in Ampere's Law?

  • Thread starter Thread starter StephenDoty
  • Start date Start date
  • Tags Tags
    Ampere's law Law
AI Thread Summary
In the discussion, the user seeks clarification on how the radial current density affects the area element dA in Ampere's Law, specifically for a solid cylindrical wire with a radially varying current density defined as J=J0*r^2. The user correctly identifies that for a cylindrical shell at radius r, the area element is dA=2*pi*r*dr, which accounts for the cylindrical geometry. The question arises about the implications of current density varying radially versus along the length of the cylinder, with the user wondering if dA would change if the current density varied in that direction. The consensus emphasizes that in this scenario, dA remains defined as 2*pi*r*dr due to the cylindrical symmetry, and the current density is specified to vary radially only. Understanding this relationship is crucial for applying Ampere's Law correctly in this context.
StephenDoty
Messages
261
Reaction score
0
Ampere's Law question (need quick answer test tomorrow)

Using Ampere's Law on a solid cylindrical wire with radius R and a current density in the direction of the symmetry axis of the wire. The current density varies radially. J=J0*r^2. What is the magnitude of the the magnetic field when r>R, outside the wire?

Using the formula B*2*pi*r= U0* \intJ dA. Which equals B*2*pi*r = U0 * \int J0* r^2 dA.

Now why does dA = 2*pi*r dr?
Can you guys give me an explanation? How does the information that the current density varies radially show that dA= 2*pi*r*dr? I am having trouble visualizing dA.

If the current density varied along the length of the cylinder wouldn't dA= pi*r^2dx? Would the current density vary along the length of the cylinder or will the current density always vary radially?

Thanks for the help.
Stephen
 
Last edited:
Physics news on Phys.org
bump...
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Question about the current components inside the Corbino disk
Replies
11
Views
1K
Problem involving Ampere's Law and Understanding
Replies
4
Views
3K
Find the Retarding Force due to Eddy Currents
Replies
5
Views
1K
Magnetostatics - Magnetic field of a nonuniform current slab
Replies
5
Views
5K
Ampere's Law - finding Magnetic Field
Replies
13
Views
3K
How does the rise in temperature of fuse wire depend upon its radius?
Replies
12
Views
1K
Magnetic field outside a conducting hollow cylinder
Replies
8
Views
5K
Magnetic energy density, and pressure due to magnetic force
Replies
23
Views
4K
Cylinder carrying volume and surface current, H field
Replies
2
Views
2K
Ampere's Law: Cylindrical conducter with varying current
Replies
9
Views
4K

Hot Threads

Recent Insights

Back
Top