1. The problem statement, all variables and given/known data
A long, straight, copper wire has a circular cross section with radius R, resistivity p and permittivity ε. If the current through the wire at any time t is sin(ωt) amperes, find the magnitude of the magnetic field B at time t a distance r from the centre of the wire for r > R.
2. Relevant equations
Ampere's Law:
μI = ∮B•dl
Possibly Law of Biot-Savart:
B = μ/4π * (Idl x r)/r^2
3. The attempt at a solution
μI = ∮B•dl
μ(sin(ωt))=∮B*dl (Since they are parallel)
μ(sin(ωt))=B∮dl (Since B is constant radially around conductor)
This is where I reach a bottleneck. I don't know how to incorporate ε (since this is a magnetic field). I assume resistivity would be used in calculating the current I, but I don't know how that ties into the sinusoidal function.
A long, straight, copper wire has a circular cross section with radius R, resistivity p and permittivity ε. If the current through the wire at any time t is sin(ωt) amperes, find the magnitude of the magnetic field B at time t a distance r from the centre of the wire for r > R.
2. Relevant equations
Ampere's Law:
μI = ∮B•dl
Possibly Law of Biot-Savart:
B = μ/4π * (Idl x r)/r^2
3. The attempt at a solution
μI = ∮B•dl
μ(sin(ωt))=∮B*dl (Since they are parallel)
μ(sin(ωt))=B∮dl (Since B is constant radially around conductor)
This is where I reach a bottleneck. I don't know how to incorporate ε (since this is a magnetic field). I assume resistivity would be used in calculating the current I, but I don't know how that ties into the sinusoidal function.
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