What is the Magnetic Field Inside and Outside a Conducting Cylinder?

H) and ∫ B.dl = µ0Ienc (for B) to find the field for the two casesIn summary, using the Biot-Savart Law and Amperes Law, one can find that the magnetic field at a distance r from the axis of a conducting cylinder with a uniformly distributed current I can be expressed as H=i*dL*sin(\theta)/4pi*r^2 for r < r0 and H=i*dL*cos(\theta)/4pi*r^2 for r > r0. To solve for H, one can use the equations ∫ H.dl round a circle (for H) and ∫ B.dl = µ0Ienc (for B) for the
  • #1
Paymemoney
175
0

Homework Statement


A conducting cylinder of radius r0 carries a current I uniformly throughout its
volume. Find an expression for the magnetic field H at a distance r from the
axis of the cylinder (a) for r < r0 , and (b) for r > r0 .

Homework Equations



Biot-Savart Law
Amperes Law

The Attempt at a Solution



I am not sure if this is correct

a) H=i*dL*sin(\theta)/4pi*r^2 for r < r0

b) H=i*dL*cos(\theta)/4pi*r^2 for r > r0

P.S
 
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  • #2
Hi Paymemoney! :smile:

(try using the X2 and X2 buttons just above the Reply box :wink:)
Paymemoney said:
a) H=i*dL*sin(\theta)/4pi*r^2 for r < r0

b) H=i*dL*cos(\theta)/4pi*r^2 for r > r0

uhh? what's dL? what's θ? :confused:

use ∫ H.dl round a circle​
 

FAQ: What is the Magnetic Field Inside and Outside a Conducting Cylinder?

1. What is a magnetic field in a cylinder?

A magnetic field in a cylinder is a region in space where magnetic forces are present due to the presence of a cylindrical object or a current flowing through a cylindrical conductor.

2. How is the magnetic field strength calculated in a cylinder?

The magnetic field strength in a cylinder can be calculated using the formula B = μ₀I/2πr, where μ₀ is the permeability of free space, I is the current flowing through the cylinder, and r is the distance from the center of the cylinder.

3. What factors affect the strength of the magnetic field in a cylinder?

The strength of the magnetic field in a cylinder is affected by the magnitude of the current flowing through the cylinder, the distance from the center of the cylinder, and the material properties of the cylinder.

4. How does the direction of the magnetic field change in a cylinder?

The direction of the magnetic field in a cylinder is always perpendicular to the direction of the current flowing through the cylinder. It follows a circular path around the cylinder, with the direction of the field determined by the right-hand rule.

5. What are the practical applications of a magnetic field in a cylinder?

A magnetic field in a cylinder has various practical applications, such as in electric motors, generators, and transformers. It is also used in medical devices, such as MRI machines, and in particle accelerators.

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