Magnetic Field in a Cylindrical Conductor

In summary, the problem involves calculating the magnetic field midway along the radius of a cylindrical conductor with a given radius and current. The correct equation to use is B = µIr / 2πa^2, which results in a magnetic field of 8.71e-6 T.
  • #1
Hypnos_16
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1

Homework Statement



A cylindrical conductor of radius R = 2.49 cm carries a current of I = 2.17 A along its length; this current is uniformly distributed throughout the cross-section of the conductor. Calculate the magnetic field midway along the radius of the wire (that is, at r = R/2).

Radius (m) = 2.49 cm = 0.0249 m = 0.01245 m (as asked)
Current (I) = 2.17 A


Homework Equations



I thought it was B = µI / 2πr because i was given a sheet of equations and this was the only one that seemed to fit it.


The Attempt at a Solution



B = µI / 2πr
B = (4π x 10^-7)(2.17) / 2π(0.01245)
B = 3.49e-5 T

Though this isn't the right answer. Not sure what's gone wrong here.
I also thought it was zero since it's a "conductor" also not right...
 
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  • #2
Not to worry, i got the answer. I was using the wrong equation.
For values of Magnetic Field inside the given radius the equation is

B = µIr / 2πa^2
B = (4π x 10^-7)(2.17)(0.01245) / 2π(0.0249^2)
B = 8.71e-6 T

In case anyone else had the same or similar problems.
 
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1. What is a magnetic field in a cylindrical conductor?

A magnetic field in a cylindrical conductor is a region of space around the conductor where a magnetic force can be observed. This force is created by the movement of electric charges, such as electrons, within the conductor.

2. How is a magnetic field created in a cylindrical conductor?

A magnetic field in a cylindrical conductor is created when an electric current flows through the conductor. This current creates a circular magnetic field around the conductor, with the strength of the field increasing as the current increases.

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

The strength of the magnetic field in a cylindrical conductor is affected by the amount of current flowing through the conductor, the distance from the conductor, and the material of the conductor. Additionally, the length and diameter of the conductor can also impact the strength of the magnetic field.

4. How can the direction of the magnetic field be determined in a cylindrical conductor?

The direction of the magnetic field in a cylindrical conductor can be determined using the right-hand rule. If the right hand is wrapped around the conductor in the direction of the current, the fingers will point in the direction of the magnetic field.

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

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

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