Copper wire magnetic field

In summary, a piece of copper wire with a resistance per unit length of 6.40e-3 ohm/m is wound into a thin, flat coil with a radius of 0.190 m. The ends are connected to a 12.0 V battery. Using the equations V = IR and B = u0 * n * I, the magnetic field strength at the center of the coil can be found by plugging in the values for R, n, and V. However, it is unclear if there is a unique solution to this problem as the length of the coil can be varied while keeping the number of turns/unit length the same, which would affect the resistance and thus the current and magnetic field strength.
  • #1
gamesandmore
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A piece of copper wire has a resistance per unit length of 6.40e-3 ohm/m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.190 m. The ends of the wire are connected to a 12.0 V battery. Find the magnetic field strength at the center of the coil.

R/L = 6.40e-3 ohm/m
r = 0.190 m
V = 12.0 V
u0 = 4pi e -7 Tm/A
B = ? T

Equations:
V = IR (I = V/R)
B = u0 * n * I
so B = u0 * n * (V/R)

I don't know where to go from here.
 
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  • #2
Start by finding L in terms of n. That may be your missing ingredient.
 
  • #3
n = turns/L
L = R/6.40e-3 ?
im lost here
 
  • #4
Did you post the question exactly?

What I'm thinking is... can't you arbitrarily make the coil longer, keeping the number of turns/unit length the same... but increasing the resistance... thereby lowering the current. And that would lower the magnetic field?

So is there a unique solution to this problem?
 

1. What is the relationship between copper wire and magnetic field?

Copper wire and magnetic field have a symbiotic relationship. When an electric current flows through a copper wire, it creates a magnetic field around the wire. Similarly, when a magnetic field is applied to a copper wire, it induces an electric current in the wire. This phenomenon is known as electromagnetic induction.

2. How does the size of the copper wire affect the magnetic field?

The size of the copper wire can affect the strength of the magnetic field it produces. A thicker wire will have a larger surface area for the electric current to flow through, resulting in a stronger magnetic field. On the other hand, a thinner wire will have a smaller surface area and thus a weaker magnetic field.

3. Does the direction of the electric current in the copper wire affect the magnetic field?

Yes, the direction of the electric current in the copper wire does affect the magnetic field. The right-hand rule can be used to determine the direction of the magnetic field, where the thumb points in the direction of the current flow and the fingers curl in the direction of the magnetic field.

4. Can copper wire be used to shield against magnetic fields?

Copper wire can be used to shield against magnetic fields to some extent. Its high electrical conductivity allows it to form a shield around the object, reducing the strength of the external magnetic field. However, other materials such as mu-metal are more effective in shielding against magnetic fields.

5. What are some real-world applications of copper wire in relation to magnetic fields?

Copper wire has many practical applications in relation to magnetic fields. It is commonly used in electric motors, generators, transformers, and other electrical devices that utilize the phenomenon of electromagnetic induction. It is also used in MRI machines and particle accelerators, where strong magnetic fields are required.

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