A straight wire segment is placed in a region known to contain a constant magnetic field of unknown strength. A current of 6 A runs through the wire, which can be turned in various directions until the force per unit length acting on it takes on a maximum value of 0.18 N/m. What is the value of the magnetic field?
To find the value of the magnetic field, you can use the equation that relates the force per unit length on a wire to the current running through the wire and the magnetic field strength.
The equation is given as:
F = B * I * L
Where:
F is the force per unit length acting on the wire,
B is the magnetic field strength,
I is the current running through the wire, and
L is the length of the wire segment.
In this case, the force per unit length (F) is given as 0.18 N/m, the current (I) is 6 A, and the length of the wire segment (L) is unspecified.
Since we want to find the value of the magnetic field (B), we need to rearrange the equation to solve for B.
B = F / (I * L)
However, since the length of the wire segment (L) is unspecified, we cannot determine the exact value of the magnetic field. Additional information is needed to find the length of the wire segment.
To find the value of the magnetic field, we can use Ampere's law and the formula for the force per unit length on a current-carrying wire in a magnetic field.
1. Start with Ampere's law:
∮ B · dl = μ₀I
Where:
- B is the magnetic field strength
- dl is an infinitesimally short length element of the wire
- μ₀ is the permeability of free space (constant)
- I is the current flowing through the wire
2. In this problem, we want to find the magnetic field strength, so we rearrange the equation to solve for B:
B = (μ₀I) / L
Where:
- L is the length of the wire segment
3. Next, we need to calculate the length of the wire segment. This can be done if we know the force per unit length acting on the wire.
4. The force per unit length on a current-carrying wire in a magnetic field is given by:
F = BIL
Where:
- F is the force per unit length
- B is the magnetic field strength
- I is the current flowing through the wire
- L is the length of the wire segment
5. Rearrange the above equation to solve for L:
L = F / (BI)
6. Substitute the given values into the equation:
L = 0.18 N/m / (6 A)
Now we have the value of L.
7. Substitute the values of μ₀, I, and L into the equation for B:
B = (μ₀I) / L
Evaluate B using the given values.
By following these steps, you should be able to calculate the value of the magnetic field.