# Magnetic Field due to Time Dependent Current

**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 * (I**dl** 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.

http://ift.tt/PiO1wd

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