Physics
Physics
Problem
In a very long straight conductor the current varies with time according to the relation , where is a positive constant. a. (i) Explain how the magnitude of the magnetic field at a fixed distance from the conductor changes with time. b. (ii) If the magnetic field at distance is at and at , find the ratio . c. (iii) At the same point, how does the energy density of the magnetic field at compare with that at ? State the factor by which it changes.Intuitive explanation
The key here is understanding how a changing current creates a changing magnetic field, which then induces an electric field in the space around the wire. You'll need to use Ampère's law to find how the magnetic field varies with distance and time, then apply Faraday's law to see how that changing field generates an induced electric field. The symmetry of the problem—cylindrical around the wire—makes the math much cleaner than it first appears.
Intuitive explanation
The key here is understanding how a changing current creates a changing magnetic field, which then induces an electric field in the space around the wire. You'll need to use Ampère's law to find how the magnetic field varies with distance and time, then apply Faraday's law to see how that changing field generates an induced electric field. The symmetry of the problem—cylindrical around the wire—makes the math much cleaner than it first appears.