A long cylindrical wire (radius = 4 cm) carries a current of 22 A that is uniformly distributed over a cross-section of the wire. What is the magnitude of the magnetic field at a point that is 0.1 cm from the axis of the wire?
Question
A long cylindrical wire (radius = 4 cm) carries a current of 22 A that is uniformly distributed over a cross-section of the wire. What is the magnitude of the magnetic field at a point that is 0.1 cm from the axis of the wire?
Solution
The magnetic field B inside a long cylindrical wire carrying a uniform current I can be calculated using Ampere's Law. The formula is:
B = (μ0 * I * r) / (2 * π * R^2)
where:
- B is the magnetic field
- μ0 is the permeability of free space, which is 4π x 10^-7 T m/A
- I is the current, which is 22 A
- r is the distance from the axis of the wire, which is 0.1 cm or 0.001 m
- R is the radius of the wire, which is 4 cm or 0.04 m
Substituting the given values into the formula, we get:
B = (4π x 10^-7 T m/A * 22 A * 0.001 m) / (2 * π * (0.04 m)^2)
Solving this equation will give you the magnitude of the magnetic field at a point that is 0.1 cm from the axis of the wire.
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