Magnitude of magnetic field at distance from central axis

In summary, the conversation discusses the calculations for the magnitude of the magnetic field at different distances from the central axis of a coaxial cable. The cable consists of an inner cylindrical conductor carrying current in one direction and an outer hollow cylindrical conductor carrying current in the opposite direction. Using the formula for magnetic fields in cylindrical conductors, B = (µ_0*I*r) / (2π*a^2), the magnitude of the magnetic field can be determined at specific distances from the central axis.
  • #1
qlzlahs
13
0

Homework Statement


A coaxial cable consists of an inner cylindrical conductor of radius R1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R2 = 0.080 m and outer radius R3 = 0.090 m. The inner conductor carries current I1 = 4.4 A in one direction, and the outer conductor carries current I2 = 6.9 A in the opposite direction. What is the magnitude of the magnetic field at the following distances from the central axis of the cable?
(μ0 = 4π × 10-7 T · m/A)
(A) At r = 0.060 m (in the gap midway between the two conductors)
(B) At r = 0.150 m (outside the cable)

Homework Equations


1. B = (μ_0/(4pi))*(Q)*(v x r)/(r^2)
2. B = ((μ_0/(2pi))*(I)*(r^2 / R^3)

The Attempt at a Solution


I'm just really not sure how to solve this. Do I plug this in the 1st equation or the second? What is r (and R)? Is there a different equation I can use?
 
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  • #2
qlzlahs said:
Do I plug this in the 1st equation or the second?
This right here is your problem. Physics is not about finding a formula to plug things in to. In order to learn you need to understand in which situations your formulae are applicable. So what do the formulae you quoted eescribe?
 
  • #3
Orodruin said:
In order to learn you need to understand in which situations your formulae are applicable

Whoops. So I think I use this equation for magnetic fields in cylindrical conductors?:
B = (µ_0*I*r) / (2π*a^2), where a is the radius and r is the distance.
 

Related to Magnitude of magnetic field at distance from central axis

1. What is the magnitude of magnetic field at a distance from the central axis?

The magnitude of magnetic field at a distance from the central axis depends on the strength of the magnetic field source, the distance from the source, and the orientation of the magnetic field. It can be calculated using the equation B = μ₀I/2πr, where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the central axis.

2. How does the distance from the central axis affect the magnitude of magnetic field?

The magnitude of magnetic field decreases as the distance from the central axis increases. This is because the magnetic field spreads out as it moves away from the source, resulting in a weaker field at greater distances.

3. What is the relationship between current and the magnitude of magnetic field at a distance from the central axis?

The magnitude of magnetic field is directly proportional to the current. This means that as the current increases, the magnetic field also increases, resulting in a stronger field at a given distance from the central axis.

4. How does the orientation of the magnetic field source affect the magnitude of magnetic field at a distance from the central axis?

The orientation of the magnetic field source can significantly impact the magnitude of magnetic field at a distance from the central axis. For example, if the magnetic field source is a straight wire, the field will be strongest directly above and below the wire. However, if the source is a loop of wire, the field will be strongest at the center of the loop.

5. Can the magnitude of magnetic field at a distance from the central axis be negative?

No, the magnitude of magnetic field at a distance from the central axis cannot be negative. Magnitude refers to the size or strength of the field, and it is always a positive value. However, the direction of the magnetic field can be negative, depending on the orientation of the field and the direction of the current.

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