Magnetic field in a infinitley long wire

[hitman0097]

Homework Statement

An infinitely long wire lies along the z axis and carries a current of 12 A in the positive z direction. A second infinitely long wire is parallel to the z axis at x = 8.2 cm.

a.)Find the current in the second wire if the magnetic field at x = 1.6 cm is zero.
b.)What is the magnetic field at x = 5 cm?

Homework Equations

F=I(LxB)

The Attempt at a Solution

I am lost with this one.

 

[rl.bhat]

What is the relevant equation for the field due to current carrying infinite long wire?

 

[kerimek]

I would approach this problem by first understanding the concept of a magnetic field and how it is affected by a current-carrying wire. I would also need to know the formula for calculating the magnetic field in this scenario, which is given by the equation F=I(LxB), where F is the force, I is the current, L is the length of the wire, and B is the magnetic field.

For part a), I would start by setting up the problem and identifying the known variables. We know that the first wire has a current of 12 A and is located along the z axis. The second wire is parallel to the z axis at x = 8.2 cm. We are also given that the magnetic field at x = 1.6 cm is zero. From this information, we can use the formula F=I(LxB) to solve for the unknown current in the second wire.

F=I(LxB)
0=I(8.2 cm x B)
0=8.2 cm x B
B=0 cm/A

Since the magnetic field at x = 1.6 cm is zero, this means that the force (F) must also be zero. Therefore, the current in the second wire must also be zero in order for the magnetic field to be zero. This makes sense, as the two wires are parallel and there would be no force between them if there is no current in the second wire.

For part b), I would use the same formula F=I(LxB) to calculate the magnetic field at x = 5 cm. We know that the first wire has a current of 12 A and is located along the z axis. The second wire is parallel to the z axis at x = 8.2 cm. We can use the formula to solve for B.

F=I(LxB)
F=12 A(8.2 cm x B)
F=98.4 cm x B
B=F/98.4 cm

Since we don't have any information about the force (F) at x = 5 cm, we cannot calculate the exact value for the magnetic field. However, we can say that the magnetic field at x = 5 cm would be non-zero, as there is a current in the second wire and the two wires are not at the same location. The exact value for the magnetic field would depend on the force between the two wires, which