The magnetic field at a distance r from a very long wire carrying current is 0.8 T. The magnetic field at a distance of 4r is_____.
Question
The magnetic field at a distance r from a very long wire carrying current is 0.8 T. The magnetic field at a distance of 4r is_____.
Solution
The magnetic field B produced by a long straight wire at a distance r from the wire is given by Ampere's law as:
B = μ0I / (2πr)
where:
- B is the magnetic field
- μ0 is the permeability of free space (4π x 10^-7 T m/A)
- I is the current in the wire
- r is the distance from the wire
From the problem, we know that the magnetic field at a distance r is 0.8 T.
We want to find the magnetic field at a distance of 4r.
We can use the same formula, but replace r with 4r:
B' = μ0I / (2π(4r))
Since the current I and the permeability of free space μ0 are constants, we can see that the magnetic field B' at a distance of 4r is 1/4 of the magnetic field B at a distance r.
Therefore, the magnetic field at a distance of 4r is 0.8 T / 4 = 0.2 T.
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