Magnetic Field With Loop and Straight Wire Help

In summary, the problem involves finding the distance r (in cm) from the center of a circular portion with radius R = 50.0 cm to the straight portion of an infinitely long wire in order to achieve a net magnetic field of zero at the center of the circular portion. The current is assumed to be equal throughout the wire, so its magnitude does not affect the solution. By treating the line and circle as separate objects and calculating the magnetic fields at the center of the loop, adjusting R can lead to a zero net magnetic field.
  • #1
GingerBread27
108
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An infinitely long wire is formed as in the diagram on your assignment. It is formed so that it has a circular portion of R = 50.0 cm and the straight portion is located at a distance r from the center of the circular portion. Find r (in cm) such that the net magnetic field at the center of the circular portion is zero.

Ok so I am confused on this problem because there is no current mentioned, and all the equations giving involve current. Then I thought that the circle could be split in two and the force of the two halves would then have to equal zero but that seems wrong as well. Please help I just don't understand :(.
 

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  • #2
I believe the arrows in the diagram are meant to be the direction of the current.

Since its all just one long wire, the current everywhere is equal.

You can treat these (line / circle) as separate objects.
 
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  • #3
There is only one wire, so I think there will be only one current. The magnitude of the current will not matter in the end or they would have told it to you.

Try solving the problem by breaking it up into a circular piece and a straight wire piece.

Calculate the magnetic field each causes in the center of the loop.

By adjusting the R the radius of the loop you should be able to get the magnetic field to equal zero.

Does this make the problem clearer?

edit:
MathStudent beat me to the punch.
 

1. How does a magnetic field form around a loop and straight wire?

When current flows through a conductor, it creates a magnetic field around it. In the case of a loop, the magnetic field lines form a continuous loop around the wire. In a straight wire, the magnetic field lines form concentric circles around the wire.

2. How does the direction of the current affect the magnetic field?

The direction of the current determines the direction of the magnetic field. If the current flows in a clockwise direction, the magnetic field lines will also be clockwise. If the current flows counterclockwise, the magnetic field lines will be counterclockwise.

3. How does the strength of the current affect the strength of the magnetic field?

The strength of the magnetic field is directly proportional to the strength of the current. This means that the stronger the current, the stronger the magnetic field will be. The strength of the magnetic field also depends on the distance from the wire, with the field becoming weaker as the distance increases.

4. What is the difference between the magnetic field of a loop and a straight wire?

The main difference between the magnetic field of a loop and a straight wire is the shape of the field. In a loop, the field forms a closed loop around the wire, while in a straight wire, the field forms concentric circles around the wire. Additionally, the strength of the field may vary depending on the distance from the wire.

5. How can the direction of the magnetic field be determined around a loop and straight wire?

The direction of the magnetic field can be determined using the right-hand rule. For a loop, point your thumb in the direction of the current and your fingers will curl in the direction of the magnetic field. For a straight wire, point your thumb in the direction of the current and your fingers will curl in the direction of the concentric circles formed by the magnetic field.

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