Wire Resistor Magnetic and Electric Field Model

Here the electric field associated with the voltage drop across a resistor is calculated* on a set of cartesian grid points located at the base of each plotted arrow. Although the size and direction of the wire's radial electric field lines depends on the local electric potential and it's capacitive connection to the environment around (here we set the potential in the resistor's center equal to ambient), an electric field component parallel to the wire establishes itself in association with the voltage drop across any resistor (or wire with finite resistance). You can reorient the model by dragging the mouse over it for a clearer look at its three-dimensional structure. Puzzler #1: Which direction is the current flowing in this resistor?

* (by integrating Coulomb's law dE=k_E dq r/r³ over the net charge distribution associated with the voltage drop across the resistor)

Any wire with a current in it, in a addition to having a bit of resistance and hence a weak electric field component in the direction of current flow, also has a magnetic field as illustrated in the animation below. Puzzler #2: Which way is the current flowing in the wire below?

• What tools and strategies would you use to carry out the calculations illustrated above?
• A similar model for the magnetic field around an inductor may be found here.
• Other recent electricity and magnetism visual puzzlers may be found here.