Magnetic field due to the current flowing in a bent wire

In summary, the problem involves calculating the magnetic field due to a bent wire at any point on the x-axis. The part of the wire parallel to the x-axis does not contribute to the field, so the focus is on the other part of the wire. The integral is used to define the different parts of the field, and considering the direction of the current before and after the bend helps to understand the situation. Sketching the field and considering simple angles can also aid in solving the problem.
  • #1
Elder1994
6
1
Homework Statement
A very thin linear conductor, which carries the current 𝐼, bends an angle 𝛼 with respect to its initial direction at some given point, as shown in the figure. Find the magnetic field 𝑩 along the line of the initial run.
Relevant Equations
$$\mathbf {B} = \int {\frac {dS \otimes r} {r^3}}$$
Hello, in this problem I'm supposed to calculate de magnetic field due to a bent wire at any point of the x-axis after the bending of the wires. It is obvious that the part of the wire that is parallel to the x-axis makes no contribution to the field so we can focus on the other part of the wire. Here I'm having some problems trying to define all the parts of the integral, I now that the dS = dx i + dy j, but I can not figure out how $$\mathbf {r}$$ looks like.

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  • #2
Helps to think about how the physics described by the equations works.

Can you sketch the field?

Taking the x-axis pointing in the direction of the current before the bend ... what happens is the current changes direction to an angle to the x axis.

So did you have a think about some easy angles ... ie. what if the bend was 90 degrees?

So what would the field along the x-axis look like if the wire was not bent at all, but, instead, was entirely at that angle?

Once you understand the situation, you'll find it easier to decide how to go forward.
 
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FAQ: Magnetic field due to the current flowing in a bent wire

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by the movement of electrically charged particles, such as electrons, and can be influenced by other magnetic fields.

How is a magnetic field created by a current flowing in a bent wire?

When a current flows through a wire, it creates a circular magnetic field around the wire. In a bent wire, the direction of the current changes, causing the magnetic field to also change direction. This results in a more complex magnetic field pattern.

What factors affect the strength of the magnetic field in a bent wire?

The strength of the magnetic field in a bent wire is affected by the amount of current flowing through the wire, the distance from the wire, and the angle of the bend. The closer the distance and the sharper the bend, the stronger the magnetic field will be.

Can the direction of the magnetic field in a bent wire be changed?

Yes, the direction of the magnetic field in a bent wire can be changed by altering the direction of the current or by changing the angle of the bend. This can be done by physically bending the wire or by using a switch to change the direction of the current.

What are some practical applications of the magnetic field created by a current in a bent wire?

The magnetic field created by a current in a bent wire has many practical applications, such as in electric motors, generators, and transformers. It is also used in MRI machines to create images of the human body and in particle accelerators to guide and control the movement of particles.

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