# Magnetic field and current homework

• oddiseas
In summary, the conversation discusses different solutions to finding the magnetic field both inside and outside a cylindrical wire with a steady current. The first solution involves using an infinitely thin coaxial surface, while the second solution involves integrating an area in cylindrical coordinates. There is confusion about the correct expression for the current and the correct domain for the magnetic field expression.
oddiseas

## Homework Statement

I have seen 4 different solutions to this question so I am starting to get confused.

A steady current I flows down a long cylindrical wire of radius R. Find the magnetic field, both inside and
outside the wire, if

(a) the current is uniformly distributed over an infinitely thin coaxial surface of radius R' < R within the wire.
(b) the current is distributed within the region r < R' such a way that j = a r3.
4

## The Attempt at a Solution

i have done part a0 but i am not sure about part b

Integrating i get I=2piar^5/5
Now other people have shown me 2pir^4/4,
but we are integrating an area da in cyllindrical coordinates so i am not sure what they are doing.

Then for the current enclosed in the cyllinder of radius R i get similarly. Then substituing the value for the constant a i get B=muIr^4/2piR^5 for r<R and B=muI/2piR for r>R

I am not sure if i have made any msiatkes

For the integral to find I, look at the units of the expression you got and of the expression other people have shown you. The two expressions have different units so they clearly can't both be right.

For the magnetic field, the split between the two expressions' domains shouldn't be at r=R. Also, in the last expression, you shouldn't have R in the denominator (but there should be something else in its place).

## 1. What is a magnetic field?

A magnetic field is a region in space where a magnet or magnetic material experiences a force. It is created by moving electric charges, such as the flow of current in a wire or the spin of electrons in an atom.

## 2. How is a magnetic field created by a current?

A magnetic field is created by the flow of current through a wire. As the electrons in the wire move, they create a circular magnetic field around the wire. The strength of the magnetic field increases with the amount of current flowing through the wire.

## 3. What is the relationship between magnetic field and current?

The strength of a magnetic field is directly proportional to the amount of current flowing through a wire. This means that as the current increases, the magnetic field also increases. Similarly, if the current decreases, the magnetic field will also decrease.

## 4. How can the direction of a magnetic field be determined?

The direction of a magnetic field can be determined using the right hand rule. If you point your right thumb in the direction of the current flow, your fingers will curl in the direction of the magnetic field. Another way is to use a compass, which will align with the direction of the magnetic field lines.

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

A magnetic field is created by the movement of electric charges, while an electric field is created by stationary electric charges. Additionally, magnetic fields are perpendicular to the direction of the current, while electric fields are parallel to the direction of the electric force.

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