Inside this resistor setup, (real world, finite sizes!) What does the E field look like inside ? <img src="./images/simple_resistor_2.png" align="center" style="width: 600px";/> 1. Must be uniform and horizontal 2. Must have some nonuniformity, due to fringing effects!

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Inside this resistor setup, what can you conclude about the current density $\mathbf{J}$ near the side walls (in steady state)? <img src="./images/shaped_resistor.png" align="center" style="width: 600px";/> 1. Must be exactly parallel to the wall 2. Must be exactly perpendicular to the wall 3. Could have a mix of parallel and perp components 4. No obvious way to decide!? Note: * Correct Answer: A (otherwise current leaks out or there's accumulation!)

**Activity:** Consider two spheres (radii $a$ and $b$ with $b$>$a$) that are constructed so that the larger one surrounds the smaller one. Between them is a material with conductivity $\sigma$. A potential difference of $V$ is maintained between them with the inner sphere at higher potential. * What is the current $I$ flowing between the spheres in terms of the known variables? * How does your result relate to Ohm's Law? Hint: Assume a uniform charge $+Q$ distributed over the inner sphere and use Gauss' Law to find $\mathbf{E}$.